Topics
4. Ratios & Proportions
topic badge
United States of America
Grade 6

4.04 Equivalent ratios on the coordinate plane

Lesson
Practice

Introduction

Previously, we learned how to make  ratio tables  . Each column in a table of values may be grouped together in the form (x,y). We call this pairing an ordered pair, which represents a specific location in the  coordinate plane  .

We will now use the ordered pairs in a ratio table to represent equivalent ratios as graphs in the coordinate plane.

Equivalent ratios on the coordinate plane

Let's consider the following table of values that represents the ratio of x to y as 1:3.

x1234
y36912

The table of values has the following ordered pairs:

(1,3),(2,6),(3,9),(4,12)

We can plot each ordered pair as a point on the coordinate plane.

-2
-1
1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
11
12
y

However, there are many more pairs of x and y values that satisfy the ratio of 1:3. In fact, there are an infinite amount of pairs.

To represent all the values in between whole numbers that represent the same ratio, we can graph a line through any two of the points.

-2
-1
1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
11
12
y

Examples

Example 1

Valerie wants to make sweet and salty popcorn. She has decided the perfect mix is 8:5 sweet to salty.

a

Complete the ratio table:

x0816243280
y
Worked Solution
Create a strategy

x and y should increase in the ratio 8:5.

Apply the idea

If x=0, then y=0 because no popcorn will be made.

Then each time x increases by 8, y increases by 5, to get:

x0816243280
y0510152050
b

Plot the ratio on the number plane.

Worked Solution
Create a strategy

Use the table from part (a) as ordered pairs for the points on the coordinate plane.

Apply the idea

Plot the points and connect all of these points to graph a line.

10
20
30
40
50
60
70
80
90
x
10
20
30
40
50
60
70
80
90
y

Example 2

Consider the following graph:

1
2
3
4
\text{Green}
1
2
3
4
5
6
7
\text{Red}
a

Which of the following could be represented by this graph and ratio?

A
For every 1 green sweet in a mix, there are 2 red sweets.
B
For every 2 green sweets in a mix, there are 1 red sweet.
Worked Solution
Create a strategy

Use the ordered pairs from the plotted points.

Apply the idea

Based from the provided graph, we can make a table of values for green sweets and red sweets.

Green sweets0123
Red sweets0246

This means that for every 1 green sweet in a mix, there are 2 red sweets, which means Option A is the answer.

b

What is the ratio of x to y in this plotted line?

Worked Solution
Apply the idea

Based on the given graph, the x-axis represents the green sweets and the y-axis represents the red sweets.

Since for every 1 green sweet in a mix, there are 2 red sweets, then the ratio of x to y from the plotted line is 1:2.

Idea summary

The graph of a ratio between two quantities is a straight line. It passes through the origin and all points found in its ratio table.

Outcomes

6.RP.A.3

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. By reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3.A

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

What is Mathspace

About Mathspace