Proportional Relationships and Equations
Student Summary
In this lesson, we wrote equations to represent proportional relationships described in words and shown in tables.
This table shows the amount of red paint and blue paint needed to make a certain shade of purple paint, called Venusian Sunset.
Note that “parts” can be any unit for volume. If we mix 3 cups of red with 12 cups of blue, you will get the same shade as if we mix 3 teaspoons of red with 12 teaspoons of blue.
| red paint (parts) |
blue paint (parts) |
|---|---|
| 3 | 12 |
| 1 | 4 |
| 7 | 28 |
| 41 | 1 |
| r | 4r |
The last row in the table shows that if we know the amount of red paint, r, we can always multiply it by 4 to find the amount of blue paint needed to make Venusian Sunset. If b is the amount of blue paint, we can say this more succinctly with the equation b=4r. So, the amount of blue paint is proportional to the amount of red paint, and the constant of proportionality is 4.
We can also look at this relationship the other way around.
If we know the amount of blue paint, b, we can always multiply it by 41 to find the amount of red paint, r, needed to make Venusian Sunset. So, the equation r=41 b also represents the relationship. The amount of red paint is proportional to the amount of blue paint, and the constant of proportionality 41.
| blue paint (parts) |
red paint (parts) |
|---|---|
| 12 | 3 |
| 4 | 1 |
| 28 | 7 |
| 1 | 41 |
| b | 41 b |
In general, when y is proportional to x, we can always multiply x by the same number k—the constant of proportionality—to get y. We can write this much more succinctly with the equation y=kx.
Visual / Anchor Chart
