# Lesson 7

Graphs of Proportional Relationships

Let's see how graphs of proportional relationships differ from graphs of other relationships.

### Problem 1

A lemonade recipe calls for \(\frac14\) cup of lemon juice for every cup of water.

- Use the table to answer these questions.
- What does \(x\) represent?
- What does \(y\) represent?
- Is there a proportional relationship between \(x\) and \(y\)?

- Plot the pairs in the table in a coordinate plane.

\(x\) | \(y\) |
---|---|

1 | \(\frac14\) |

2 | \(\frac12\) |

3 | \(\frac34\) |

4 | 1 |

### Problem 2

There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point \((6, 47.94)\) is shown on the graph below.

- What is the constant of proportionality in this relationship?
- What does the constant of proportionality tell us about the situation?
- Add at least three more points to the graph and label them with their coordinates.
- Write an equation that represents the relationship between \(C\), the total cost of the subscription, and \(m\), the number of months.

### Problem 3

The graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix. Label the point \((1, k)\) on the graph, find the value of \(k\), and explain its meaning.

### Problem 4

Select **all** the pieces of information that would tell you \(x\) and \(y\) have a proportional relationship. Let \(y\) represent the distance in meters between a rock and a turtle's current position and \(x\) represent the time in minutes the turtle has been moving.

\(y = 3x\)

After 4 minutes, the turtle has walked 12 feet away from the rock.

The turtle walks for a bit, then stops for a minute before walking again.

The turtle walks away from the rock at a constant rate.

### Problem 5

What information do you need to know to write an equation relating two quantities that have a proportional relationship?