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# The Guide to Graphing Proportional Relationships

Get the free Graphing Proportional Relationships worksheet and other resources for teaching & understanding how to Graph Proportional Relationships

## Here’s how to Graph Proportional Relationships

Graphing Proportional Relationships can be completed by using values from a table or from an equation that contains a Proportional Relationship. Proportional Relationships are relationships that contain ratios that have a Constant of Proportionality. The Constant of Proportionality is the multiplier that relates the variables together. Finding the Constant of Proportionality involves multiplying or dividing between the variables to find the number that relates the variables. You can write the Constant of Proportionality by using the equation y=kx where k is the Constant of Proportionality.

Common Core Standard: 7.RP.2

## Breaking down the Rules for Proportional Relationship Graphs

Graphing Proportional Relationships can be completed by using a table that contains a Proportional Relationship. Proportional Relationships will be connections that contain proportions that have a Constant of Proportionality. The Constant of Proportionality is the multiplier that relates the factors together. Finding the Constant of Proportionality consists of finding the number that relates the two variables in the table. You can discover the Constant of Proportionality by utilizing the equation y=kx where k is the Constant of Proportionality.

## 3 Quick Steps for solving Proportional Relationships Graphs

1. Plot the points from the table into the graph.
2. Find the rate at which the values increase as you go up each cell in the table.
3. The multiple that increases the values is the Constant of Proportionality.

## Graphing Proportional Relationships Practice Problems Quiz

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Proportional Relationships Quiz

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What is the Constant of Proportionality of the following table?

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What is the Constant of Proportionality of the following table?

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What is the Constant of Proportionality of the following table?

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What is the Constant of Proportionality of the following table?

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What is the Constant of Proportionality of the following table?

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## Watch the video Explanation of our Graphing Proportional Relationships Worksheet

Watch our free video on how to Graph Proportional Relationships. This video shows how to solve problems that are on our free Graphing Proportional Relationships worksheet that you can get by submitting your email above.

Watch the free Graphing Proportional Relationships video on YouTube here: Graphing Proportional Relationships Video

Video Transcript:

This video is about graphing proportional relationships. You can get the graph proportional relationships worksheet used in this video for free by clicking on the link in the description below. In order to show you how to solve proportional relationship in graphs, we’re going to do a couple practice problems from our graphing proportional relationships worksheet.

The first problem we’re going to do on our proportional relationship graph worksheet is number two. This problem gives us a table, a graph, and asks us to solve for the constant of proportionality. The first thing we’re going to do is we’re going to use our table to complete our proportional relationship graph on the right. The first thing we can do is we can label our axes on our graph. We know that the x-axis is going to be minutes. We know this axis is going to be minutes and we know that the y-axis is going to be feet. In order to graph this, we use the values that are given to us in our proportional table here. Our first point is going to be 0 0. We put a dot on 0 0. The second point that is given to us is 1 minute and then 2 feet. We go over to our proportional relationship graph and we go to 1 minute and then up to two feet and we put our second dot. The third point we can put on our graph is minutes is two and feet is four. We go over to two minutes and then up to four feet and we put our third dot, fourth point is going to be minutes is three and then feet is six, we put a dot there and then our last point gives us minutes is four, four minutes and then eight feet. We put our last dot there. Now that our proportion relationship has been graphed, we can find the constant of proportionality. The constant of proportionality is given as the equation k equals y divided by x, and k is the constant of proportionality, y is the y values, and x is the x values. Our x axis is minutes so we know the minutes represent the x values and the y axis is feet. We know feet are represented by the y axis. In order to solve our formula k equals y divided by x we can use any column from our table as long as we put feet in for y and minutes in for x. I’m going to use this fourth column, which gives us three minutes and six feet so our feet is six. We know that’s the y value the minutes are three, we know that’s the x value. To simplify this, we’re going to do 6 divided by 3 which is 2.  Now we know that the constant of proportionality is 2 feet every minute and that’s going to be the solution.

The last problem we’re going to complete on our proportional graphs worksheet is number three. The first step is to use our table to complete the graphs of proportional relationships on the right. Again, we’re going to use the values from each column to plot the points on our graph here. The first step is to label our axes so we’re going to label hours on the x-axis and then miles on the y-axis in order to complete the proportion relationships graph. We’re going to use the columns from the table to plot our points. The first column gives us 0 0. That’s going to be our first point, second column gives us 1 hour is 3 miles, we put a dot there, this third column gives us 2 hours is 6 miles, and then 3 hours is nine miles and then four hours. We go to hour four and then up to 12 miles, and then five hours, and then 15 miles and then finally six hours which is 18 miles. Now that our proportional relationship has been graphed, we can find the constant of proportionality. We know that the constant of proportionality is equal to the y values divided by the x values and we know that the x values are represented by hours and the y values are represented by miles. We can take any column that we want to find the constant of proportionality. I’m going to use column number four. This column gives us miles, which is our y value as nine, this is 9 miles divided by our hours column which is 3. It’s 3 hours and then when you reduce this, you’ll get 9 divided by 3. It’s three miles for every one hour and that’s going to be our solution. You can try all these practice problems by downloading the free graphing proportional relationships worksheets above.

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