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3.04 Equivalent ratios on the coordinate plane


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:


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...


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.


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

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








Use ratio reasoning with equivalent whole-number ratios to solve real-world and mathematical problems by:• Creating and using a table to compare ratios.• Finding missing values in the tables. • Using a unit ratio. • Converting and manipulating measurements using given ratios. • Plotting the pairs of values on the coordinate plane.

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