Ratios and the Coordinate Plane

Lesson 4.03

After completing this lesson, you will be able to say:

• I can plot pairs of values that represent equivalent ratios on the coordinate plane.

• I can solve real-world and mathematical problems involving ratio and rate using coordinates

Ratios as Ordered Pairs

Let’s see how a coordinate plane can show the equivalent ratios

Given the ratio: for every 3 cans of fruit, there are 2 cans of soup.

make a table of equivalent ratios

Fruit Soup

3 2

6 4

9 6

12 8

15 10

Let’s choose the fruit cans to be on the x-axis and the soup cans to be on the y-axis.

Now we can use the table to set the equivalent ratios up as coordinate points.There are 5 points (3, 2), (6, 4), (9, 6), (12, 8), and (15, 10)

Now you can use the points to plot them on the coordinate plane.

One thing you should notice is that only the first quadrant is needed, as there are no negative cans of soup or frui

The Graph

Example

Melissa is creating designs on her gift boxes for her group members, as they all worked so hard. Because there is only room for 12 designs, for every 7 diamonds, she places 5 stars. Let’s create an equivalent ratio table and plot those ratios to see how many stars are needed if there are 28 diamonds.

1. Create the table of equivalent ratios 2. Plot the points

Try it

A department store has socks on sale for 2 pairs for $5. Use a ratio table to find the cost of 6 pairs of socks and then plot the coordinates on a plane.

Check your work

The ordered pairs are (2, 5), (4, 10), and (6, 15)

Applying Rates

You can determine the unit rate in a relationship by the points plotted on a coordinate plane

The coordinate plane shows the distance traveled by a person. Use the coordinates to determine the miles per hour.

Applying Rates

Determine the coordinates

From the graph, you can see that there are three ordered pairs, (3, 6), (5, 10), and (7, 14). In order to determine the unit rate, you must use the ordered pairs to determine the ratio for the two quantities.

Create a table

Determine the Unit Rate

Because all of the ratios are equivalent, only one pair is needed. So for every 3 hours of time, this person traveled 6 miles.

Try It!

Sarah bought 3 game controllers at Games Plus for $27. Determine the unit price for a game controller. Then plot the relationship on a coordinate plane to show other prices, depending on the number of controllers purchased.

Check your work

Find the Unit Rate

Create ordered pairs and plot the points

Now that you completed this lesson, you should be able to say:

• I can plot pairs of values that represent equivalent ratios on the coordinate plane.

• I can solve real-world and mathematical problems involving ratio and rate using coordinates