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Graphing Proportional Relationships

8.EE.B.5
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Aligned To Common Core Standard:

Grade 8 Number System - 8.EE.B.5

How to Graph Proportional Relationships Suppose your teacher asks you to graph a proportional relationship between two variables (x and y) with the unit rate of 0.4, which is a change in a single unit of x will cause a change of 0.4 units in y. Let's think about some potential values between x and y. Remember that here we have an independent value x and an independent value y. What that means is that some value of y will be equal to a constant multiplied with the value of x. If we were to express this using an expression, it would be: Y = kx (K equals to any constant number) X, Y = (0, 0), (1, 0.4), (2, 0.8), (3, 1.2), (4, 1.6), (5, 2) If you were to draw a graph of these values, you would know that it is going to make a straight line. It shows that the graph has a proportional relationship. This series of lessons and worksheets will help students learn how to graph and identify graphs of proportional relationships.

Printable Worksheets And Lessons


  • Faster Paces Step-by-Step Lesson- Two boys are riding bikes. Which one moves at a faster pace?

  • Guided Lesson - All the problems compare a graph to an equation. So kids find it easier to graph the equation. Yet others find it easier to determine the equation of the graph.

  • Guided Lesson Explanation - I like equations and for the answers I put everything into an equation. I will come back and work on this one to have a graph comparison version later this month.

  • Independent Practice - It's a big battle royale of graphs versus equations.

  • Matching Worksheet -This one is pretty easy because it's matching. I would insist on everyone showing their work.




Homework Sheets

Compare the graph and the equation without any change.

  • Homework 1 - The graph below represents the number of cakes that Eric makes in a day. The equation (right) represents how many cakes Lewis makes in a day. Who makes cakes at a faster rate?
  • Homework 2 - When both equations are constant. This makes it very easy to compare.
  • Homework 3 - The graph below represents the number of trips made by Truck A over 7 days. The equation below represents the number of trips made by Truck B over 7 days. Who takes more trips over the course of a week?



Practice Worksheets

The color of the line dot here was requested by many teachers. It shows up well on Smart boards.

  • Practice 1 - The equation represents the rate at which Jackson sells books. Who sells more books over 5 hours?
  • Practice 2 - The equation represents the rate at which Sarah travels on her scooter. If both Jessie and Sarah were to travel for 7 straight days, who would you predict to travel further?
  • Practice 3 - Over a day, who watches more movies?



Math Skill Quizzes

Because of the size of the graph, I can only get two questions on each page.

  • Quiz 1 - Who uses strawberries at a faster rate?
  • Quiz 2 - Who eats more cookies over the course of a week?
  • Quiz 3 - The equation represents the number of greeting cards made by the Kim and the number of sheets used. Who uses fewer sheets?


How to Spot Proportional Relationships on Graphs

When two variables have a proportional relationship, they will exist in a ratio to one another that is constant. This means that when they are visualized on a line graph, first they will form a line that passes through the origin (0, 0). They will exist in some form of the equation y = kx. To translate this for you as x increase, so does y. If the y value decreases, then so does the x value. As a result, they are relentless proportion with one another. Regardless of how big or small their values are, these variables will always be relative to one another.