4.09 Equivalent ratios on the coordinate plane
For the following x:y ratios and their corresponding table of values, plot the points on a coordinate plane:
| x | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| y | 3 | 4 | 5 | 6 |
| x | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| y | 6 | 8 | 10 | 12 |
| x | 3 | 6 | 9 | 12 |
|---|---|---|---|---|
| y | 1 | 2 | 3 | 4 |
| x | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| y | 8 | 12 | 16 | 20 |
For each of the following proportional relationships:
Complete the table of values.
Plot the points on a coordinate plane.
Sketch the graph of the proportional relationship between x and y.
The ratio of x:y is 1:3.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y |
The ratio of x:y is 4:1.
| x | 4 | 8 | 12 | 16 |
|---|---|---|---|---|
| y |
The ratio of x:y is 2:3.
| x | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| y |
The ratio of x:y is 1:5.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y |
The ratio of x:y is 2:6. Graph this proportional relationship on a coordinate plane.
Consider the following graph:
Complete the ratio table by using the points shown in the graph:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
Valerie wants to make sweet and salty popcorn. She has decided the perfect mix is 8:5 sweet to salty.
Complete the ratio table.
Graph the proportional relationship on a coordinate plane.
| \text{Sweet} \left(x\right) | 0 | 8 | 16 | 24 | 32 | 80 |
|---|---|---|---|---|---|---|
| \text{Salty} \left(y\right) |
A tank is being filled. The tank fills up at a rate of 2 liters per hour.
Complete the table of values:
| \text{Number of hours passed} \left(x\right) | 0 | 1 | 2 | 3 | 4 | 4.5 | 10 |
|---|---|---|---|---|---|---|---|
| \text{Amount of water in tank} \left(y\right) |
Graph the proportional relationship on a coordinate plane.
What ratio did you graph in part (b)?
The following graph shows the proportion of red sweets and green sweets in a mix:
Find the number of red sweets for every 1 green sweet in a mix.
The following graph shows the number of patients that are seen over time:
What ratio has been plotted?
Write a statement to describe the number of patients being seen evey hour.
The following graph shows the distance traveled over time:
Describe how the distance traveled changes over time.
State the ratio of distance to time.
The following graph shows the ratio of the number of cups of strawberries to the number of cups of raspberries required in a recipe:
What ratio has been plotted?
Describe the relationship between the number of cups of strawberries and the number of cups of raspberries required.