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.
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.
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:
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:
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?
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.