4.09 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.
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.
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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.
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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.
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 $x$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$5 sweet to salty.
Complete the ratio table:
sweet ($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...
Question 3
Consider the following graph:
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.
AFor every $2$2 green sweets in a mix, there is $1$1 red sweet.
BWhat is the ratio of $x$x to $y$y in this plotted line?
$2:1$2:1
A$1:2$1:2
B