## Graphing Proportional Relationships

#### 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.