California 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.

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

$x$x |
$1$1 | $2$2 | $3$3 | $4$4 |
---|---|---|---|---|

$y$y |
$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 $xy$`x``y`-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**.

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

Complete the table of values below:

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

Loading Graph...Draw the graph of the proportional relationship between $x$

`x`and $y$`y`.Loading Graph...

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

Complete the ratio table:

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

Loading Graph...

Consider the following graph:

Loading Graph...

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.

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

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

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

B- 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

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.

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.