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

    Loading Graph...

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

    Loading Graph...

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

    Loading Graph...

Question 3

Consider the following graph:

Loading Graph...

  1. Which of the following could be 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
  2. What is the ratio of $x$x to $y$y in this plotted line?

    $2:1$2:1

    A

    $1:2$1:2

    B

 

Outcomes

6.RP.3

Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems.

6.RP.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.

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