An axis in mathematics is defined as a line that is used to make or mark measurements. The x and y-axis are two important lines of the coordinate plane.

These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.

Here, x represents the location of the point with respect to the x-axis and y represents the location of the point with respect to the y-axis.The origin is where the two axes intersect and is written as (0,0). Let us learn how to plot a point on the graph by using the X- and Y-axis.

Here, the x-coordinate of B is 3. So we will start from the origin and move 3 units to the right on x-axis.

And thus we have plotted our point B(3,4) on the graph using the axes. To understand how to represent a linear equation on the graph using the X- and Y-axis,.

Now, let’s build a table to represent the corresponding values of y for different values of x and create their ordered pairs: The next step is to plot these ordered pairs on the coordinate plane graph.

Question 1: Which of the following points lie on the x-axis.

Answer: Since the coordinates lying on x-axis have their y coordinate zero (0), the following points will lie on x-axis: (4, 0) (−5, 0) (8, 0) (6, 0).

If the given points are (3,2) and (2,3), then plot these two points on the X- and Y-axis. Also, find out the point where the straight line going through these points meets the x-axis.

Similarly we can plot the point (2,3). Now, we can join both points with a straight line when we have plotted both points.

Question 3: For a linear equation y = 2x + 6, find the point where the straight line meets y-axis on the graph. Answer: On y-axis, the x-coordinate of the point is 0.

y = 2(0)+6 = 0 + 6 = 6. So the straight line of the equation y = 2x + 6 meets the y-axis at (0,6).

Attend this Quiz & Test your knowledge. Why are the X- and Y-axis important.

The X- and Y-axis are essential for a graphical representation of data. These axes make the coordinate plane.

Graphical representation helps in solving complicated equations. How is the coordinate plane formed.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis (or ordinate).

What are quadrants in a graph.

These regions are called quadrants. The quadrants are denoted by roman numerals and each of these quadrants have their own properties.

How are the X- and Y-axis different.

The X and Y axis form the basis of most graphs. These two perpendicular lines define the coordinate plane.

In this system, the axes are the following: The grid below displays the X and Y axes.

For example, the red data point is at (3, 5). The X and Y axes have the following properties in the Cartesian coordinate system:

It always has an X value = 0, while the Y value is the point where the line crosses the Y Axis. For example, in the graph below, the Y-intercept for the green line is (0, 4), and for the red line it is (0, -2).

That’s the basic usage for the X and Y axis. Now, let’s learn how different graphs use them to gain a better understanding of what they want to convey.

Learn more about using equations to draw lines in my Guide to the Slope Intercept Form of Linear Equations. In graphing and statistics, the X and Y axis each displays different kinds of information depending on the type of graph.

As we go through some common graphs, pay particular attention to the axes. Notice how each graph type has both an X and Y axis but uses them differently.

Scatterplots are visually and functionally the most like the Cartesian coordinate system, except they don’t display the gridlines. Use these graphs to plot pairs of X and Y data points.

For example, in the graph below, the X axis represents height, and the Y axis denotes weight. Each dot’s (X, Y) coordinate represents an individual’s height and weight combination.

A statistical convention is that when you have a pair of variables and one variable explains the changes in the other variable, you include the explanatory variable on the X axis and the outcome variable on the Y axis. Scatterplots can superimpose a fitted regression line for simple regression models.

Y-intercepts for regression lines are one of the parameters that the model estimates. Learn more about Scatterplots and Linear Regression Lines.

These graphs are fantastic for understanding a distribution’s center, spread, and shape. The most common type of histogram has vertical bars, as shown below.

The Y axis represents counts, percentages, or probabilities of the observations falling within each bin. The histogram below displays body fat percentages horizontally and vertically depicts the number of times (i.e., frequency) observations fall within each bin.

Occasionally, you’ll see rotated histograms that switch the axes. Those histograms have horizontal bars.

Time series plots show how a variable changes over time. Most commonly, the X axis displays the time, while the Y axis displays the outcome variable that you are tracking.

For example, the time series plot below tracks the number of COVID cases vertically, while it shows time in days horizontally. There appears to be a COVID surge near the end of the dataset.

Learn more about Time Series Plots. Bar charts help us understand categorical and other discrete variables.

The Y axis represents counts or a summary value, such as the average. For example, the bar chart below displays the categories of delivery statuses and peak/off peak times horizontally.

The proportion of late deliveries increases during peak times.

Box plots allow you to compare the center and spread of continuous data across groups or categories. Typically, these graphs display the groups along the X axis and the continuous outcome variable on the Y axis.

For example, the box plot below displays teaching method horizontally and the test scores vertically. Teaching method 4 has the highest median score.

Learn more about Box Plots. By learning how a graph uses these two axes, you’ll understand what it wants to convey.

The x-axis and y-axis are two lines that create the coordinate plane.

I’m sure you’ve heard that a million times, but it might hard for you to remember which one is which.

Can you hear the “rhymes. ” x to the left and y to the sky.

All the time students ask about “Where can I buy research paper. ” – I advise them this company website.

Use these tricks to help your remember which axis is which. Once you know them using these clues, you’ll never forget them again.

Reminder: the x-axis really runs left and right, and the y-axis runs up and down. Notice the arrows at the ends of the blue and purple lines.

So even though we only show the coordinates going up to values of 10, they can be extended as large (or small) as you want.

Share this trick with her and then she can tell the whole class. With your help, everyone will undestand the x-axis and y-axis.

In the grid above, we can plot points and graph lines or curves. Hopefully these little rhymes will help you to remember the correct directions for the x-axis and y-axis.

How about our explanation of the coordinate plane through Disney’s Pirates of the Caribbean. Don’t miss it.

The graph of x and y-axis also referred to as the graph x and y axis, are two crucial lines in the 2-D plane. A graph can represent data on both the horizontal and vertical axes.

A graphical depiction of data requires the X- and Y-axis. The coordinate plane is made up of these axes.

Complicated equations can be solved more easily using graphics. To better understand, let’s learn more about the line graph x and y axis in Mathematics, the table, the charts, and answer a few cases.

The two axes, the x-axis, and the y-axis, that makes up a graph’s coordinate plane can be used to define a graph x and y-axis. The x-axis and y-axis stand in for the horizontal and vertical axes.

X and Y Axis.

The graph of the y-axis is also referred to as the ordinate. Any point on the coordinate plane is well defined by an ordered pair, which is written as (x-coordinate,y-coordinate) or (x,y), where x-coordinate denotes a point on the x-axis or at a perpendicular angle from the y-axis and y-coordinate denotes a point on the y-axis or at a perpendicular angle from the x-axis.

Quadrants in a Graph.

Example: Number of minutes of commercials in one hour of television since 2009-. Year Since 2009.

10.75. 4.

12.25. 6.

We use an ordered pair to find any point on the coordinate plane. The ordered pair is written as (x-coordinate,y-coordinate) or (x, y), where x-coordinate denotes a point on the x-axis or perpendicular distance from the y-axis and y-coordinate denotes a point on the y-axis or perpendicular distance from the graph of x-axis.

Using years as the x-axis and the number of minutes of commercials in one hour of television as the y-axis, depict these points as follows on the x and y chart.

A horizontal x-axis and a vertical y-axis make up the line graph. These axes often cross around the bottom of the y-axis and the left end of the x-axis because the majority of line graphs only deal with positive numerical values.

A data type is listed next to each axis. The x-axis could represent days, weeks, quarters, or years, for instance, while the y-axis displays revenue in dollars.

Line Graph with X and Y-axis.

The set of all points (x, y) in a coordinate plane such that x is related to y by the relation R is known as the graph of a relation R. It is possible to graph a relation (relation graph) made up of infinitely many ordered pairs of numbers using just point plotting.

Illustration: The given diagram shows a relation graph. $R=\{(2,5),(4,3),(6,1),(2,7)\}$.

Relation Graph.

Draw a line graph to represent the data from the table. Hours.

Ans:.

A number of weeks vs rainfall. Plot the graph from the given data.

Rainfall – 23 21 17 19 24.

Plot a line graph from the given data of x and y respectively.

Draw the line graph showing the following table.

Colours. Yellow.

of People. 28.

Draw the line graph:.

Height. 0.

A line graph has two axes: a horizontal x-axis and a vertical y-axis (vertical). The sites where the axes connect each indicate a distinct type of data, and (0, 0).

In the given article we have discussed the X and Y graphs. Definition of X and Y graphs and graph x and y-axis are given with the graph of relation in this article.

The x-axis and y-axis are two important lines that make a graph. A graph consists of a horizontal axis and a vertical axis where data can be represented.

In a graph, the x-axis is horizontal and the y-axis is vertical. In this article, we will learn about the x-axis and y-axis and we will also see the graph plotter with points along with solving a few examples.

Any point on the coordinate plane can be described by an ordered pair, which is written as (x-coordinate, y-coordinate) where the x-coordinate denotes a point on the x-axis and the y-coordinate denotes a point on the y-axis. The ordinate or “y-axis” is another name for the y-axis and another name for the x-axis is known as the “abscissa” or “x graph.”.

A graph is made up of two crucial lines called the x and y axes. In a graph, data can be represented on both the horizontal and vertical axes.

The x-axis and y-axis on the graph are these two horizontal and vertical lines or axes, respectively. As the origin is where the x- and y-axes intersect.

X-axis and Y-axis Graph.

As a result, each answer to the linear equation can be represented as a distinct point on the equation’s graph. Lines parallel to the y-axis and the x-axis, respectively, represent the graphs of x = a and y = a.

Any point on the x-axis has coordinates of (x,0), where x is the abscissa and 0 is the ordinate. As a result, each point on the x-axis has an ordinate of 0.

Take the linear equation y = 2x+1 as an example. Now, create a table with two columns for the values of x and y to graph this equation then draw a graph as follows:.

So, if when x = 0. y = 2(0) + 1.

Similarly, when x = 1, y = 3 and when x = 2, y = 5.

Graph Plotter.

So for locating the points on the graph, we just have to point to the x and y-axis.

For this, the x-axis will be zero and on the y-axis, we have to go up to 1.

Similarly, other points can be drawn. In the end, join these points.

Graph Using Plotter Points.

The table for the X and Y graph shows the population of a city from 2015 to 2020 as:.

Graph Plotter (Example 1).

Each point is located on the graph indicated by an ordered pair with the x-axis coming first and the y-axis coming second. The chart is as follows:

Graph (Example 1).

Daniel’s teacher assigns him a maths task with x and y axes that requires him to graph the points (3, 2) and (2, 3) and draw a line that connects them. Can you point to the location where it intersects the x-axis.

Ans: The graph can be used to plot the points as displayed.

Graph.

Draw a coordinate system and place the coordinates (1,2), (0,4), and (-1,-3) on it. Are all of the points on a line.

State true or false. On the y-axis, the x coordinate is nonzero and the y coordinate is zero.

The x-axis is a vertical line. Ans: False.

Ans: True. The y-axis is a vertical line.

Any point on the coordinate plane is well defined by an ordered pair where the ordered pair is written as (x-coordinate, y-coordinate) or (x,y), where the x-coordinate represents a point on the x-axis or perpendicular distance from the y-axis and the y-coordinate represents a point on the y-axis or perpendicular distance from the x-axis.

The x-axis is also known as abscissa or x graph whereas the y-axis is also known as ordinate or y graph. Later, we have also seen how to plot the graph by using linear equations.

What is the x-axis in coordinate geometry. In coordinate geometry, when we draw a graph on the coordinate plane, then the horizontal line in that graph is known as the x-axis.

In coordinate geometry, when we draw a graph on the coordinate plane, then the vertical line in that graph is known as the y-axis. The numbers marked on the y-axis are called the y-coordinates (or ordinate).What is the use of x-axis and y-axis.

When two or more points are joined, a straight-line segment can be obtained. Hence, x-axis and y-axis are the most important aspects of a Cartesian Coordinate System.What are collinear points in coordinate geometry.

A pair of numbers written within brackets and separated by a comma is called an ordered pair, for example (x,y), where x and y are any numerical values (positive or negative).What is the equation of the x axis and y axis. The equation of x-axis is y=0 and the equation of y-axis is x=0.

In coordinate geometry, when we draw a graph on the coordinate plane, then the horizontal line in that graph is known as the x-axis. The numbers marked on the x-axis are called the x-coordinates (or abscissa).What is the y-axis in coordinate geometry.

The numbers marked on the y-axis are called the y-coordinates (or ordinate).What is the use of x-axis and y-axis. x-axis and y-axis are used to mark the coordinates of a point on a coordinate plane.

Hence, x-axis and y-axis are the most important aspects of a Cartesian Coordinate System.What are collinear points in coordinate geometry. The set of points that lie on the same straight line are called collinear points.What is an ordered pair.

The equation of x-axis is y=0 and the equation of y-axis is x=0. What is the x-axis in coordinate geometry.

The numbers marked on the x-axis are called the x-coordinates (or abscissa). In coordinate geometry, when we draw a graph on the coordinate plane, then the horizontal line in that graph is known as the x-axis.

What is the y-axis in coordinate geometry. In coordinate geometry, when we draw a graph on the coordinate plane, then the vertical line in that graph is known as the y-axis.

In coordinate geometry, when we draw a graph on the coordinate plane, then the vertical line in that graph is known as the y-axis. The numbers marked on the y-axis are called the y-coordinates (or ordinate).

x-axis and y-axis are used to mark the coordinates of a point on a coordinate plane. When two or more points are joined, a straight-line segment can be obtained.

x-axis and y-axis are used to mark the coordinates of a point on a coordinate plane. When two or more points are joined, a straight-line segment can be obtained.

What are collinear points in coordinate geometry. The set of points that lie on the same straight line are called collinear points.

What is an ordered pair. A pair of numbers written within brackets and separated by a comma is called an ordered pair, for example (x,y), where x and y are any numerical values (positive or negative).

What is the equation of the x axis and y axis. The equation of x-axis is y=0 and the equation of y-axis is x=0.

A graph scale, or simply scale, refers to a set of numbers that indicate certain intervals on a graph used for measurement. There are many different types of graphs, including bar graphs, histograms, line graphs, and many more.

Choosing a graph’s scale is an important aspect of data presentation. Depending on the scale chosen, the presented data may provide a comprehensive picture of the data, or it could misrepresent the data.

Graph type selection is also very important, since different graph types excel at presenting different types of data. For example, line graphs are helpful for emphasizing differences between values.

Pay attention to the type of graph you select to represent data. if you are unsure what type of graph to use, plot the same data using various types of graphs to get a better grasp of the pros and cons of using each graph type.

each interval along the axis represents the same incremental increase. For example, each mark on the x- and y-axes of the coordinate plane represents 1 unit, as shown in the figure below.

For example, each interval on the y-axis could represent 2, or even 10 units, while each interval on the x-axis represents 1 unit. As long as the intervals have consistent magnitudes within each axis (i.e.

Consider the graph of the line y = x. If we were to use the standard coordinate plane, where each tick mark represents 1 unit, we can clearly see the graph of the line y = x in the figure below (left).

Although the above example is extreme, it illustrates the importance of graph scales. There are many cases in which data can be obscured by an improperly selected scale.

In such cases, a typical coordinate plane in which each tick mark represents 1 unit would be too large, and it may not show behavior in the graph we would otherwise see with different scaling. A coordinate plane is only one example of graph scales.

However, the same principles can be carried through many different types of graphs. Below is an example of a line graph in which the x-axis and y-axis have different intervals that are specifically chosen to ensure that the data presented is clear.

A logarithmic scale is one in which each interval represents the subsequent power of 10. On a logarithmic scale, the numbers 10 and 100, and 30 and 300 are equally spaced (in a linear scale, 10 and 20, and 30 and 60, would be equally spaced).

Because there are so many ways to present data, it is important to understand what type of graph(s) to use, as well as what scale to use, in order to most effectively present the data.

Your students may have encountered ordered pairs last year, but it’s a good idea to start by reviewing how to locate a point on a grid from an ordered pair. A day spent plotting coordinates that fall in a straight line will be a day well spent.

(5.G.A.1). Materials: Poster paper or a way to display a coordinate grid publicly for the class.

Preparation: Draw a large coordinate grid that the entire class can see. Label the x- and y-axes from 0 through 10.

At this level, students will begin to see the relationship between equations and straight-line graphs on a coordinate grid. Key Standard: Interpret an equation as a linear function, whose graph is a straight line.

Materials: Poster paper or a way to display a coordinate grid publicly for the class. straightedge.

Preparation: Draw a coordinate grid where all students can see it. Label the x- and y-axes from 0 through 10.

Prerequisite Skills and Concepts: Students should know about ordered pairs and locating points on a grid. They should also be able to recognize and interpret an equation.

Reinforce the need for students to work carefully so their graph is accurate. When you assess students’ progress, keep the number of exercises small enough that they have time to complete each step without rushing.

We often want to show data in the form of a graph. Usually, graphs have two axes, like this:.

The horizontal axis is labeled “x-axis”, a name which we often use for it. The vertical axis is labeled “y-axis”.

Mathematicians often put these in an italic font, so that they are easier to distinguish from the same letters being used in the words around them.

Suppose we want to plot a point on the graph. We will plot one for which the value of x is 1 and the value of y is 2.

We draw a line vertically upwards. We find the value 2 along the y-axis.

Where these lines intersect is where we mark the point:.

On graph paper, they would be on the pre-ruled grid lines on the paper. Computers do them automatically and do not usually show them:.

We will keep the gridlines for this illustration.

When we are plotting on graph paper, we usually use a cross as the symbol, because it is convenient and enables us to show the point accurately at the intersection of the two lines of the cross. Computers may use a variety of symbols for plotting: circles, squares, diamonds, etc.

For example, this is a diamond point symbol:.

Sketch a graph to show the following (genuine) weights and heights of a group of men:.

The values of x and y for a point on a graph are called the coordinates. Sometimes this is hyphenated: co-ordinates.

The coordinates of a point are shown like this (x-value, y-value). Hence the first man in the table above is plotted at coordinates (1.75, 76.4).

The point at coordinates (0,0) is called the origin of the graph.

This only makes sense if the points are ordered in some way, usually when the x-axis variable is time. There would be no value in doing this for the heights and weights.

Sometimes the points are omitted altogether, just leaving the line:.

Sketch a line graph to show the numbers of deaths associated with volatile substance abuse (VSA) in the UK between 1983 and 1999:.

The following line graph does not represent health data, but an idealised relationship:.

We can see how this proportionality works by looking at how y changes with x. We can draw vertical lines one unit of x apart:.

The vertical distance on the y scale between the points where these verticals meet our line is the increase in y for a one unit increase in x:.

We call this the gradient or slope of the line:. increase in y slope = –––––––––– increase in x.

We have. 10 – 5 5 slope = –––––– = –– = 5 2 – 1 1.

This line goes through the point with coordinates (0,0), the origin. When x = 0, y = 0.

This line does not go through the origin. Its slope is 3, because y increases by 3 units when x increases by 1.

The equation of this line is y = 5 +3x:.

The general equation of a straight line is. y = intercept + slope × x.

y = c + mx. or the other way round as.

Just to be awkward, statisticians often write. y = a + bx.

They are numbers which tell us which of the many possible lines we have.

This line has a negative slope, where y decreases as x increases. We can see that when x = 1, y = 17, and when x = 2, y = 14.

increase in y 14 – 17 –3 slope = –––––––––– = –––––––– = ––– = –3 increase in x 2 – 1 1 Exercise: straight line graphs. Sketch graphs of the following lines: y = x y = 2 + 0.5x y = 5 – x.

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This page maintained by Martin Bland. Last updated: 3 October, 2007.

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Make sure you have a scatter chart in Excel.

You’ve discovered a subtle, but important difference in how Excel charts data. Generally, Line charts treat their horizontal (X) axis as categorical data, while Scatter (XY) charts treat theirs as numeric data.

There are two ways to address this shortcoming. The most efficient is to use a Scatter chart with lines connecting your points.

However, there are times when you may want to use a Line chart (e.g. your horizontal axis are dates and you want to use the built in aggregation for major and minor units to days/weeks/months).

use =NA() for the “blanks”, and Excel won’t plot the values). Excel will provide an axis point for each value, it just won’t be plotted.

Here’s an example:.

EDIT: Also, FWIW, your chart doesn’t change values past Line Speed of 300. Unless you have a specific business reason to extend out to 750, it’s worth considering shortening the horizontal axis to 300, and allowing the differences to be emphasized.

Before we get into reflections across the y-axis, make sure you’ve refreshed your memory on how to do simple vertical and horizontal translations. One of the most basic transformations you can make with simple functions is to reflect it across the x-axis or another horizontal axis.

1) Graph y=−f(x)y = -f(x)y=−f(x). 2) Graph −f(x)-f(x)−f(x).

In order to do this, the process is extremely simple: For any function, no matter how complicated it is, simply pick out easy-to-determine coordinates, divide the y-coordinate by (-1), and then re-plot those coordinates. That’s it.

The best way to practice drawing reflections across the y-axis is to do an example problem: Example:

Remember, the only step we have to do before plotting the −f(x)-f(x)−f(x) reflection is simply divide the y-coordinates of easy-to-determine points on our graph above by (-1). When we say “easy-to-determine points” what this refers to is just points for which you know the x and y values exactly.

Below are several images to help you visualize how to solve this problem. Step 1: Know that we’re reflecting across the x-axis.

When drawing reflections across the xxx and yyy axis, it is very easy to get confused by some of the notations. So, make sure you take a moment before solving any reflection problem to confirm you know what you’re being asked to do.

Remember, pick some points (3 is usually enough) that are easy to pick out, meaning you know exactly what the x and y values are. In this case, let’s pick (-2 ,-3), (-1 ,0), and (0,3).

While the xxx values remain the same, all we need to do is divide the yyy values by (-1).

And that’s it. Simple, right.

In some cases, you will be asked to perform horizontal reflections across an axis of symmetry that isn’t the x-axis. But before we go into how to solve this, it’s important to know what we mean by “axis of symmetry”.

It can be the x-axis, or any horizontal line with the equation yyy = constant, like yyy = 2, yyy = -16, etc. Finding the axis of symmetry, like plotting the reflections themselves, is also a simple process.

This is because, by it’s definition, an axis of symmetry is exactly in the middle of the function and its reflection. The best way to practice finding the axis of symmetry is to do an example problem.

Find the axis of symmetry for the two functions shown in the images below. Again, all we need to do to solve this problem is to pick the same point on both functions, count the distance between them, divide by 2, and then add that distance to one of our functions.

Now, by counting the distance between these two points, you should get the answer of 2 units. The last step is to divide this value by 2, giving us 1.

Looking at the graph, this gives us yyy = 5 as our axis of symmetry. Let’s take a look at what this would look like if there were an actual line there:

You may learn further on how to graph transformations of trigonometric functions and how to determine trigonometric functions from their graphs in other sections.

Just as there are rules of grammar in composition, there are rules of graphing that help to visualize data for your audience. A well-designed graph should not need much explanation because the graph itself should make the trends in the data visually apparent.

Each of the following terms carries an important meaning. Imagine that we want to make a graph of the amount of rainfall that occurs at different times of year.

Therefore, rainfall is the dependent variable and time of year is the independent variable. In some graphs, you may have more than one dependent variable, but never more than one independent variable.

The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line). The x and y axes cross at a point referred to as the origin, where the coordinates are (0,0).

Each axis needs a scale to show the range of the data on that axis. The low end of the scale may be zero or a round number value slightly smaller than the smallest data point.

The scale is measured off in major and minor tick marks. Typically the scale runs from low to high in easily counted multiples like 10s, 50s, 100s, etc.

Each axis needs a descriptive axis label indicating which variable is represented. For example, the y-axis label might read “Total Rainfall” and the x-axis label might read “Month”.

If you are measuring rainfall, people won’t know if you mean inches, millimeters, gallons, etc. unless you include the units.

Typically, each independent measurement represents a point on the graph. If there are multiple data sets being plotted on the same graph, each set should be represented by a unique symbol.

Typically the answer is yes if the data points are part of a series of measurements of the same thing over a period of time, for example. The implication is that the values do not drop back to zero between measurements.

In some cases, the relationship may not be linear, but exponential or logarithmic, or some other mathematical function, so a curve might be more appropriate than a line. However, there should be a reason why a particular curve is chosen.

For example, your legend might indicate that green lines or bars represent rainfall in the tropics while brown lines or bars represent rainfall in the desert region. Colors or patterns should be used to help convey information, but should not be used simply for decoration.

If the colors were reversed, would this be better or worse. Why.

The type of data you are presenting may be better suited for one kind of graph than another. For example, if your measurements are periodic samples of an ongoing event, like rainfall each day, then a line with points helps to convey that message.

If you are trying to visually display the pieces of a whole, a piechart might be a good choice. Each point on the graph might represent a single data point, or the average of a collection of measurements at that point.

Typically the error around the mean is expressed as the standard deviation, but with small sample sizes, the standard error is sometimes used. The title should be a brief statement describing the subject of the graph, but should not describe or interpret the results.

For example, bars should not be 3-D unless the third dimension adds information.

There are three types of graphical symmetry you may be responsible for: x-axis, y-axis, and origin. Knowing the properties of symmetry can help you when sketching complex graphs.

you can fold the paper it is graphed on along the x-Axis and the halves of the graph will line up. If the ordered pair (x, y) is a solution to the equation and the equation is symmetric to the x-axis, then (x, -y) will also be a solution.

An equation or function that is symmetric with respect to the y-axis has (x, y) and (-x, y) as solutions. Likewise, if you switch -x for x in the original equation, the result should be the original equation when simplified.

Equations or functions that are symmetric to the origin have ordered pairs (x, y) and (-x, y). If you switch -x for x and -y for y in the original equation and simplify, if you get the original equation, it is symmetric with respect to the origin.

The Graphical Symmetry Foldable can be added to an interactive notebook to help students remember key concepts. Be sure to rotate it when printing or copying.

It is said that a picture is worth a thousand words. Likewise, a graph can often be used to better understand relationships between variables.

Along the horizontal axis, we start at the origin or a zero. To the right numbers increase and to the left numbers decrease.

On the vertical axis, we also start at the origin or zero. The numbers increase as we go up and decrease as we go down.

Combining the horizontal and vertical axes allow us to look at the relationships between variables in two-dimensional space. While we will, at times, use all four quadrants, we typically spend most of our time in the first quadrant or the space where both the horizontal and vertical variables are positive.

If the various values of x and y are given, the points can be plotted on the graph.

Once the points are plotted, the dots can be connected to form a line or curve.

In our example, there is a linear relationship between x and y. We can express the same information, using an equation.

In modeling causal relationships, the value of an endogenous or dependent variable depends upon the value of other variables in the model. When graphing, we typically place the dependent variable on the vertical or y-axis.

These are typically graphed on the x (or horizontal) axis.

For example, as income increases, the amount people will consume also increases.

As the price of a good falls, the number of people willing to buy the good increases.

When x increases by one, y increases by 2. The slope of a line is determined by taking the change in the vertical amount divided by the change in the horizontal amount.

In our example, as x increases by 2, y increases by 4, so the slope would a positive 2.

From an equation, we are able to derive the points in a table by plugging in the values of x and computing the value of y.

A curve will have different slopes at different points along the curve. By taking the change in y over the change in x, we are able to get an estimate of the curve at that point.

If we compute the slope over a distance around three, we find that the slope from 0 to 6 is 12, and from 2 to 4 is also 12.

If we were to draw a tangent line (a line that touches the curve only at one place) where x equals 3, we could then compute the slope of the tangent. In doing so, we would find the slope is again 12.

One of the key tools in economics is marginal analysis. As economists look at relationships between variables, they want to know what will be the change in one variable, given a change in another variable.

Thus, being able to compute the slope of the tangent tells us the marginal change in the dependent variable.

One powerful mathematical tool in calculus is called the derivative. The derivative tells us the slope of the curve at a particular point.

The derivative simply tells us the change in y given a very small change in x, or in other words the slope of the curve at a particular point. Given the function, Y = 4 + 2×2, the first derivative gives us a slope of the tangent at a given point.

The derivative gives us the slope of the curve. ΔY / ΔX = slope of the curve.

First derivative = ΔY / ΔX = 4x. Slope of the tangent when x = 3 is 4(3) = 12.

In our example, the intercept value is increased from 2 to 4.

Increases (decreases) in the slope causes the curve to be steeper (flatter).

We are able to find the market equilibrium either by graphing or algebraically. If on the demand side, we are given Price = 50 – 2 (Quantity Demanded) and on the supply side, we are given Price = 10 + 2 (Quantity supplied).

Even without graphing the curves, we are able to see that at a price of $30, the quantity demanded equals the quantity supplied.

If we graph it, we find that at price of 30 dollars, the quantity supplied would be 10 and the quantity demanded would be 10.

An alternative way, is to solve the problem algebraically. Since at equilibrium the quantity supplied equals the quantity demanded and the price will be the same for both.

P = 50 – 2Qd and P = 10 + 2 Qs. Set the two equations equal.

Our first step is to get the Qs together, by adding 2Q to both sides. On the left hand side, the negative 2Q plus 2Q cancel each other out, and on the right side 2 Q plus 2Q gives us 4Q.

P = 50 – 2Qd and P = 10 + 2 Qs. Set the two equations equal.

+ 2Q + 2Q. 50 = 10 + 4Q.

We can subtract 10 from both sides and are left with 40 = 4Q. The last step is to divide both sides by 4, which leaves us with an equilibrium Quantity of 10.

Set the two equations equal. 50 – 2 Q = 10 + 2 Q.

50 = 10 + 4Q. -10 = -10.

40/4 = 4/4 Q. 10 = Q.

We can subtract 10 from both sides and are left with 40 = 4Q. The last step is to divide both sides by 4, which leaves us with an equilibrium Quantity of 10.

Equilibrium Q = 10. P = 50 – 2Qd or P = 10 + 2 Qs.

P = $30 or P = $30. Math as a tool enables economists to determine the optimums.

Finding the slope of a curve can be extremely useful when determining the maximum or minimum. For example, let’s say a company uses labor to produce a product, called widgets.

If the company wants to find how many workers will maximize their output, they would look at the point where the slope of the curve goes to zero. In our example if the company wanted to maximize output, it would use eight workers to do so.

Charts and graphs are frequently used to display information. A pie chart shows the portion or relative magnitude of the total amount that is made up by each of the components.

Data: 2008 Statistical Abstracts (2007 Data). A bar chart shows the amount or magnitude of each item by the length of the item.

Data: 2008 Statistical Abstract of the United States (2004 data) A time series displays the data values over time. Time is along the horizontal axis and the observations are evenly spaced, such as annually, quarterly, or monthly.

Data: 2008 Statistical Abstracts. Cross sectional data looks at various segments of a population at a point in time.

As seen from the data, those with more education tend to have greater earnings and lower unemployment rates.

Panel data combines cross sectional information and time series. This graph displays the unemployment rate by race over time.

Another useful tool in economics is the growth rate. A growth rate measures the percentage change in a variable, and is calculated by taking the difference between the new value and the old value then dividing the change by the old value.

For example, if $200 is invested in the bank on January 1 and on December 31st the amount has grown to 240 dollars, then the percentage increase is calculated by taking the $40 increase divided by the original $200 to find the growth rate of 20 percent.

Example:. Invest $200 on Jan 1 and have $240 on Dec.

Step 1: Observe the given graph and choose a nonzero point {eq}(x,y) {/eq}. Check to see if either {eq}(x,-y), \ (-x,y),\text{ or }(-x,-y) {/eq} are also on this graph.

Step 2a: If {eq}(x,-y) {/eq} is also on this graph, check a few other points to see if this same pattern occurs. If so, the graph is symmetric with respect to the x-axis.

Step 2b: If {eq}(-x,y) {/eq} is also on this graph, check a few other points to see if this same pattern occurs. If so, the graph is symmetric with respect to the y-axis.

Step 2c: If {eq}(-x,-y) {/eq} is also on this graph, check a few other points to see if this same pattern occurs. If so, the graph is symmetric with respect to the origin.

Symmetric: A graph is symmetric if, when a reflection is applied, it looks exactly the same. There are three main types of symmetry that we will consider:.

When a graph is symmetric with respect to the x-axis, this means that if the point {eq}(x,y) {/eq} exists on our graph, the point {eq}(x,-y) {/eq} also exists. This is because reflecting across the horizontal x-axis will yield the same graph and so all positive y-values will map to negative y-values, and vice versa.

When a graph is symmetric with respect to the y-axis, this means that if the point {eq}(x,y) {/eq} exists on our graph, the point {eq}(-x,y) {/eq} also exists. This is because reflecting across the vertical y-axis will yield the same graph, and so all positive x-values will map to negative x-values, and vice versa.

An example of such a graph would be the following:.

When a graph is symmetric with respect to the origin, this means that if the point {eq}(x,y) {/eq} exists on our graph, the point {eq}(-x,-y) {/eq} also exists. This is because reflecting across the line {eq}y=x {/eq} (which is equivalent to reflecting about the origin) will yield the same graph.

The graph is also said to be odd when this occurs. An example of such a graph would be the following:.

We will now go through three examples step-by-step.

Step 1: Choose a nonzero point {eq}(x,y) {/eq}, and see if either {eq}(x,-y), \ (-x,y),\text{ or }(-x,-y) {/eq} are also on this graph.

{/eq} Which of the points {eq}(1,2), \ (-1, -2),\text{ or }(-1,2) {/eq} are also on this graph. In this case, we see that the point {eq}\textit{(-1,2)} {/eq} is also on here, so we will proceed to Step 2c.

Step 2c: Check a few other points to see if this same pattern occurs.

Is {eq}(-2,4) {/eq} also on this graph. Yes.

Analyze the graph shown below, and determine if it is symmetric with respect to the x-axis, y-axis, or origin:.

Let’s choose the point {eq}(2,2). {/eq} Which of the points {eq}(2,-2), \ (-2, 2),\text{ or }(-2,-2) {/eq} are also on this graph.

Step 2b: Check a few other points to see if this same pattern occurs.

Is {eq}(-4,8) {/eq} also on this graph. Yes.

Analyze the graph shown below, and determine if it is symmetric with respect to the x-axis, y-axis, or origin:.

Let’s choose the point {eq}(-3,3). {/eq} Which of the points {eq}(-3,-3), \ (3,3),\text{ or }(3,-3) {/eq} are also on this graph.

Step 2a: Check a few other points to see if this same pattern occurs.

Is {eq}(-12,-6) {/eq} also on this graph. Yes.

This short section explains how to read and understand information from a graph. A graph is a way of showing complicated information in a clear easy to understand way.

A graph usually has a vertical axis (y-axis) and horizontal axis (x-axis). Each axis need to be clearly marked with what is being measured: time, CD4 count etc.

All graphs should have a clear title.

If the graph is being used to show data rather than just a general trend or idea, then the units being measured need to be included on a scale, ie hours or years for time, cells/mm3 for CD4 counts. This scale needs to be shown in even measurements.

Showing data on a graph is called plotting. An example of how one person’s CD4 results after starting treatment could be plotted is shown in Figure 1.

To make results clearer, a line showing an average of the results is often added to make the general trend appear more clearly. Although the actual counts go up and down a lot, the average trend in the example above shows CD4 count increasing by about 200 copies/mm3 over 18 months.

For example the average CD4 counts of a group of 100 people after treatment could look exactly the same. The only difference in a graph that is showing more than one set of results, is that the numbers of people at each time point should also be included underneath each time.

The mathematical term for number is n. In Figure 2, the results are for a group of 100 people, but either not all the people have completed the study or some people have dropped out.

If the number of participants at the end of a study is much lower than at the beginning, you need to know what happened to the other people. Graphs should also show the range of variation within a group, not just the ‘average’.

See Figure 3.

This can either show: The graph should state which range is being shown.

Scales Always check the scale on a graph. If it doesn’t start at zero, then the change shown may look more impressive than it really is.

If early results of a study are being shown, the numbers at each time point may much lower after further time points. Last updated: 22 July 2009.

1 Distance Time Graphs Time is always plotted on x axisDistance is always plotted on y axis To figure average speed, divide distance by time. 2 Distance-time graphs 2) Horizontal line = Stopped, not moving 40 30 2010 4) Diagonal line downwards = returning to start Distance (meters) 3) Steeper diagonal line = faster the motion Time/s Diagonal straight line = moving at constant speed.

Curving downwards – shows decrease in speed, It is still accelerating – change in speed. 4 40 30 20 10 Distance (meters) Time/s What is the speed during the first 20 seconds.

How far is the object from the start after 60 seconds. What is the speed during the last 40 seconds.

5 How to calculate slope Slope = y2 – y1 X2 – X1 Rise divided by Run25- 5 = 20 Slope = 4 m/s. 6 Question What does the slope of a distance vs.

It tells you the SPEED. 7 Leroy is the fastest.

time graph for 3 runners. Who is the fastest.

He completed the race in 3 hours. 8 Speed Time Graphs Time in plotted on X-axisSpeed or velocity is plotted on Y-axis Shows acceleration.

10 80 60 40 20 Velocity m/s T/s How fast was the object going after 10 seconds. What is the acceleration from 20 to 30 seconds.

How far did the object travel all together.

2nd-Nonlinear-Axis. Last Update: 9/17/2021.

The graph below is a single layer where both the bottom X axis and the top X axis are displayed. The bottom X axis is wavelength in nanometers as present in the raw data.

Each tick label on top axis is calculated with formula: Energy (ev) = 1240 / Wavelength (nm).

Here are the steps:.

You have to use the Layer Management dialog as follows:. Note: In Layer Management dialog, Apply button must be clicked after making changes.

When creating a Formula for axis labels, use “x” to refer to the current axis, whether it is an X, Y or Z axis.

In the example above, top X and bottom X axes use the same settings. Only tick labels on top are calculated using the formula.

show ticks in a reciprocal scale as the image below, you need to add a new linked layer with top axis showing.

Here are the steps.

Top axis range will update accordingly.

Here are the steps:.

Keywords:link, formula, equation, frequency, wavelength, energy, reciprocal, non-linear, scale.

Transformations >. Reflection over the x-axis is a type of linear transformation that flips a shape or graph over the x-axis.

Every point below the x-axis is reflected to its corresponding position above the x-axis. Contents: Reflection over the x-axis for:

Example question #1: Reflect the following set of coordinates over the x-axis: (-4, 6), (-2, 4), (0, 0), (2, 4), (4, 6). Solution: Step 1: Place a negative sign in front of each y-coordinate:

Step 2: (Optional) Plot both sets of coordinates (your original points and the ones from Step 2) to make sure you negated correctly. You can easily do this on Desmos.com: Just enter coordinates into the left hand column and check the “Label” box:.

More formally: When a function f(x) is reflected over the x-axis, it becomes a new function g(x) = – f (x).

Solution: Step 1: Place a negative sign in front of the right-hand side of the function: f(x) = x2 – 3 becomes g(x) = – (x2 – 3). Step 2: Remove the parentheses, carrying through the negative sign: g(x) = -x2 + 3.

Note: I’m using f(x) and g(x) here to name the functions, but you can name them anything you like (or use whatever names your instructor is using). The important part of the formula is the expression on the right hand side.

The above matrix A reflects a point (defined by column vector x) over the x-axis. For example, let’s say you had a point (1, 3) and wanted to reflect it over the x-axis.

Joyce, D. Some Linear Transformations on &Ropf.

Math 130 Linear Algebra. Retrieved April 17, 2021 from:.

Any point in a 2D space is represented by x and y coordinates as an ordered pair, either of which can be zero, positive or negative. If either value is zero, the point is represented as the following:

If both x and y coordinates are non-zero, the point lies somewhere on the 2D coordinate plane in one of its four quadrants. Consider point M in the coordinate plane here.

So, its x coordinate is (1), and its y coordinate is (2). Together, its (x, y) coordinates are represented on the 2D coordinate plane as the following:

Point M is in Quadrant 1. Consider point N in the coordinate plane here.

So, its x coordinate is (-3), and its y coordinate is (-4). Together, its (x, y) coordinates are represented on the 2D coordinate plane as the following:

Point N is in Quadrant 3.

The biggest use for graphs is that it allows us to actually visualize the relations and functions that we are working with. In order to do this, we simply graph the ordered pairs in the relation or function on the Cartesian coordinate plane.

Graph the relation \(R = \{(-3, 5), (-2, 3), (0, 12), (1, -2), (6, 5)\}\).

Graph the function \(\{(−3,−3),(1,1),(5,2),(7,2)\}\).

But in the last section, we discussed how functions can be described by rules using equations, instead of a short list of ordered pairs. This means that in order to create ordered pairs to graph the function, we must choose our own inputs for this.

\((x, f(x)).\). These ordered pairs will act as our ordered pairs \((x, y)\) that we use for plotting, where we treat \(f(x)\) as the \(y\) values.

These are what we will use to graph a function \(f(x)\) that we determine using an equation. Graph \(f(x) = 2x-1\) using a table.

\(\begin{array} {|c|c|}\hline \text{Inputs \((x)\)} & \text{Outputs \(f(x)\)} & \text{Ordered Pairs \((x, f(x))\)} \\ \hline & & \\ \hline & & \\ \hline & & \\ \hline & & \\ \hline & & \\ \hline \end{array}\). Step 2: Choose several inputs to use to create ordered pairs.

Add these inputs to the table. In this example, we will use \(x\) values -2, -1, 0, 1, 2.

\(\begin{array} {|c|c|}\hline \text{Inputs \((x)\)} & \text{Outputs \(f(x)\)} & \text{Ordered Pairs \((x, f(x))\)} \\ \hline -2 & & \\ \hline -1 & & \\ \hline 0 & & \\ \hline 1 & & \\ \hline 2 & & \\ \hline \end{array}\). Step 3: Compute the outputs \(f(x)\) corresponding to each input \(x\) by plugging the \(x\) value into the rule for \(f(x)\).

\(\begin{array} {|c|c|}\hline \text{Inputs \((x)\)} & \text{Outputs \(f(x)\)} & \text{Ordered Pairs \((x, f(x))\)} \\ \hline -2 & 2 \cdot (-2) – 1 = -5 & \\ \hline -1 & 2 \cdot (-1) – 1 = -3 & \\ \hline 0 & 2 \cdot 0 – 1 = -1 & \\ \hline 1 & 2 \cdot 1 – 1 = 1 & \\ \hline 2 & 2 \cdot 2 – 1 = 3 & \\ \hline \end{array}\).

add to table. \(\begin{array} {|c|c|}\hline \text{Inputs \((x)\)} & \text{Outputs \(f(x)\)} & \text{Ordered Pairs \((x, f(x))\)} \\ \hline -2 & 2 \cdot (-2) – 1 = -5 & (-2, -5) \\ \hline -1 & 2 \cdot (-1) – 1 = -3 & (-1, -3) \\ \hline 0 & 2 \cdot 0 – 1 = -1 & (0, -1) \\ \hline 1 & 2 \cdot 1 – 1 = 1 & (1, 1) \\ \hline 2 & 2 \cdot 2 – 1 = 3 & (2, 3) \\ \hline \end{array}\).

Based on the table we have created, we need to plot the pairs (-2, -5), (-1, -3), (0, 1), (1, 1), and (2, 3):.

Recall that when a function is defined by an equation, we have a lot of inputs for \(x\) to choose from. We account for this on the graph by sketching a picture of a graph suggested by the points plotted.

Be sure to continue the line beyond the last points to indicate that we could have used even more inputs.

Graph the function \(f(x) = x^2 + 3\) using a table. The points used on the table may vary, but the graph should look the same.

Creating visually compelling and informative graphs is an essential skill for anyone working with data in Excel. When it comes to graph design, the position of the x-axis plays a crucial role in how data is interpreted and understood.

However, fear not. In this comprehensive guide, we will explore the step-by-step process of moving the x-axis to the bottom of the graph in Excel, allowing you to create graphs that are not only visually appealing but also enhance the clarity of your data presentation.

Whether you’re a beginner or an experienced Excel user, mastering this technique will empower you to create impactful graphs that effectively communicate your data insights. So, let’s dive in and discover how to take your Excel graphing skills to the next level by repositioning the x-axis to the bottom.

Before you dive into customizing your graph, it’s essential to ensure that your data is well-organized and prepared for visualization. Take the time to arrange your data in a logical and structured manner within your Excel worksheet.

Sort your data: Arrange your data in a consistent order, such as ascending or descending, based on the variables you want to analyze. This helps establish a clear relationship between the data points.

Focus on including the essential variables and values that you want to visualize. Group-related data: If your data consists of multiple categories or groups, consider grouping them together to facilitate easier analysis and interpretation.

By organizing your data thoughtfully, you lay a solid foundation for creating meaningful and visually appealing graphs that effectively convey your intended message.

The default positioning of the X axis in Excel may not always align with your visualization goals. By adjusting the X axis position, you can optimize the graph’s layout and improve its overall readability.

To begin modifying the X-axis, first, identify it on your graph. Typically, the X-axis is the horizontal axis at the bottom of the graph.

To access the formatting options for the X axis, right-click on the selected X axis. A context menu will appear, providing various formatting choices.

Within the “Format Axis” window, you’ll find an array of options to adjust the X-axis position. Look for settings such as “Axis Position,” “Horizontal Axis Crosses,” or “Axis Labels.” These settings enable you to shift the X-axis to your desired location.

In this case, we’ll switch it to the low position. Moving the X axis to the bottom of the graph often provides a clearer visual representation, especially when dealing with negative values on the Y axis.

After making the necessary changes to the X-axis position, click “Apply” or “OK” to confirm the modifications. Take a moment to observe the updated graph, paying attention to how the X-axis labels have now been repositioned.

Remember, the adjustment of the X-axis position is just one aspect of graph customization. Continue exploring various formatting options, such as axis labels, data markers, gridlines, and chart titles, to further refine the visual impact of your graph.

This simple adjustment significantly enhances graph clarity and improves the accessibility of your data. Remember to explore additional customization options and continuously refine your graph design skills to create visually captivating and impactful visualizations.

Frequently you need to calculate the distance between two points in a plane. To do this, form a right triangle using the two points as vertices of the triangle and then apply the Pythagorean theorem.

states that if given any right triangle with legs measuring a and b units, then the square of the measure of the hypotenuse c is equal to the sum of the squares of the legs: a2+b2=c2. In other words, the hypotenuse of any right triangle is equal to the square root of the sum of the squares of its legs.

Example 5: Find the distance between (−1, 2) and (3, 5). Solution: Form a right triangle by drawing horizontal and vertical lines through the two points.

The length of leg b is calculated by finding the distance between the x-values of the given points, and the length of leg a is calculated by finding the distance between the given y-values. Next, use the Pythagorean theorem to find the length of the hypotenuse.

Generalize this process to produce a formula that can be used to algebraically calculate the distance between any two given points. Given two points, (x1, y1) and (x2, y2) , then the distance, d, between them is given by the distance formulaGiven two points (x1, y1) and (x2, y2), calculate the distance d between them using the formula d=( x 2− x 1)2+( y 2− y 1)2.:

Example 6: Calculate the distance between (−3, −1) and (−2, 4). Solution: Use the distance formula.

This improves readability and reduces the chance for errors. Answer: 26 units.

Try this. Calculate the distance between (−7, 5) and (−1, 13).

Example 7: Do the three points (1, −1), (3, −3), and (3, 1) form a right triangle.

In other words, if you can show that the sum of the squares of the leg lengths of the triangle is equal to the square of the length of the hypotenuse, then the figure must be a right triangle. First, calculate the length of each side using the distance formula.

Answer: Yes, the three points form a right triangle. In fact, since two of the legs are equal in length, the points form an isosceles right triangle.

In Select Data chart option we can change axis values or switch x and y axis If we want to edit axis or change the scaling in the graph we should go to Format Axis options.

In the example we have a chart with Years on x-axis and Sales values on the y-axis: Figure 1.

To change x axis values to “Store” we should follow several steps: Figure 2.

Figure 3. Change horizontal axis values.

Select the new x-axis range. Figure 5.

To learn how to change vertical axis values, we should follow almost similar steps as in the example above:. Figure 6.

Figure 7. How to edit y axis.

How to change y axis. Figure 9.

To change the scale on the graph we should go to Format Axis options. In our example, we will change the minimum scale to 15,000 and maximum scale to 55,000 on the vertical axis.

If we want to change the axis scale we should:. As a result, the change in scaling looks like the below figure:

How to change the scale. Another interesting chart feature that we will learn is how to switch x and y axis.

Figure 11. Switch x and y axis.

Figure 12. How to swap x and y axis.

In the following example, we want to change sales values to yearly sales values per store (upper table). Figure 13.

Figure 14. Change the chart data source.

Expand the chart data source. Figure 16.

Most of the time, the problem you will need to solve will be more complex than a simple application of a formula or function. If you want to save hours of research and frustration, try our live Excelchat service.

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