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Lin needs to mix a specific shade of orange paint for the set of the school play. The color is a mixture of red and yellow paint.
Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs.
| cups of red paint | cups of yellow paint |
|---|---|
| 2 | 3 |
| 6 | |
| 12 | |
| 12 | |
| 21 | |
| 1 | |
| 1 |
Use the values in the table to create two graphs that can represent the relationship between cups of red paint and cups of yellow paint.
Describe the relationship between cups of red paint and cups of yellow paint in as many ways as you can.
Pause here for a discussion.
Lin writes this equation to figure out the amount of yellow paint she will need if she knows the amount of red paint being used. In this equation,
Equations are very useful for representing the relationship in a set of equivalent ratios. Here is an example.
A cider recipe calls for 3 green apples for every 5 red apples. We can create a table to show some equivalent ratios.
We can see from the table that
| green apples ( |
red apples ( |
|---|---|
| 3 | 5 |
| 6 | 10 |
| 9 | 15 |
| 12 | 20 |
We can write equations to describe the relationship between
When we know the number of green apples and want to find the number of red apples, we can write:
In this equation, if
We can use this equation with any value of
When we know the number of red apples and want to find the number of green apples, we can write:
In this equation, if
We can use this equation with any value of
To help us see the relationship between the two quantities, we can also create two graphs, one graph that corresponds to each equation.
A graph that represents a ratio of two quantities. The graph has a horizontal axis labeled number of green apples and the numbers 1 through 15 are indicated, The vertical axis is labeled number of red apples and the numbers 1 through 20 are indicated. The following four points are indicated on the graph: 3 comma 5, 6 comma 10, 9 comma 15, and 12 comma 20.
A graph that represents a ratio of two quantities. The graph has a horizontal axis labeled number of red apples and the numbers 1 through 15 are indicated. The vertical axis is labeled number of green apples and the numbers 1 through 20 are indicated. The following three points are indicated on the graph: 5 comma 3, 10 comma 6, and 15 comma 9.
The dependent variable is the result of a calculation.
For example, a boat travels at a constant speed of 25 miles per hour. The equation
A graph of 10 points plotted in the coordinate plane with the origin labeled "O". The horizontal t axis is labeled "time in hours". The numbers 0 through 10, in increments of 2, are indicated, and there are vertical gridlines midway between. The vertical axis is labeled "distance traveled in miles". The numbers 0 through 250, in increments of 25, are indicated, and there are horizontal gridlines midway between. The data are as follows: 1 comma 25. 2 comma 50. 3 comma 75. 4 comma 100. 5 comma 125. 6 comma 150. 7 comma 175. 8 comma 200. 9 comma 225. 10 comma 250.
The independent variable is used to calculate the value of another variable.
For example, a boat travels at a constant speed of 25 miles per hour. The equation
A graph of 10 points plotted in the coordinate plane with the origin labeled "O". The horizontal t axis is labeled "time in hours". The numbers 0 through 10, in increments of 2, are indicated, and there are vertical gridlines midway between. The vertical axis is labeled "distance traveled in miles". The numbers 0 through 250, in increments of 25, are indicated, and there are horizontal gridlines midway between. The data are as follows: 1 comma 25. 2 comma 50. 3 comma 75. 4 comma 100. 5 comma 125. 6 comma 150. 7 comma 175. 8 comma 200. 9 comma 225. 10 comma 250.