Tennessee 6 - 2020 Edition
3.04 Equivalent ratios on the coordinate plane
Lesson

Each column in a table of values such as a ratio table may be grouped together in the form $\left(x,y\right)$(x,y). We call this pairing an ordered pair, which represents a specific location in the coordinate plane. We can use the ordered pairs in a ratio table to represent equivalent ratios as graphs in the coordinate plane.

#### Exploration

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

 $x$x $y$y $1$1 $2$2 $3$3 $4$4 $3$3 $6$6 $9$9 $12$12

The table of values has the following ordered pairs:

$\left(1,3\right),\left(2,6\right),\left(3,9\right),\left(4,12\right)$(1,3),(2,6),(3,9),(4,12)

We can plot each ordered pair as a point on the $xy$xy-plane.

However, there are many more pairs of $x$x and $y$y values that satisfy the ratio of $1:3$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.

Graphing ratios

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.

#### Practice questions

##### Question 1

The ratio of $x:y$x:y in a proportional relationship is $1:3$1:3.

1. Complete the table of values below:

 $x$x $y$y $1$1 $2$2 $3$3 $4$4 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
2. Plot the points in the table of values.

3. Draw the graph of the proportional relationship between $x$xand $y$y.

##### QUESTION 2

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

1. Complete the ratio table:

 sweet ($x$x) salty ($y$y) $0$0 $8$8 $16$16 $24$24 $32$32 $80$80 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
2. Plot the ratio on the number plane.

##### Question 3

Consider the following graph:

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

For every $1$1 green sweet in a mix, there are $2$2 red sweets.

A

For every $2$2 green sweets in a mix, there is $1$1 red sweet.

B

For every $1$1 green sweet in a mix, there are $2$2 red sweets.

A

For every $2$2 green sweets in a mix, there is $1$1 red sweet.

B
2. What ratio has been plotted?

$2:1$2:1

A

$1:2$1:2

B

$2:1$2:1

A

$1:2$1:2

B

### 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.