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 $xy$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.
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.
Draw the graph of the proportional relationship between $x$xand $y$y.
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.
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.
For every $2$2 green sweets in a mix, there is $1$1 red sweet.
What is the ratio of $x$x to $y$y in this plotted line?
$2:1$2:1
$1:2$1:2