# Lesson 4

Comparing Proportional Relationships

Let’s compare proportional relationships.

### Problem 1

A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies.

EZ Excavation gives its prices in a table.

dirt (cubic yards) |
cost (dollars) |
---|---|

8 | 196 |

20 | 490 |

26 | 637 |

Happy Hauling Service gives its prices in a graph.

- How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning.
- Calculate the rate of change for each relationship. What do they mean for each company?
- If the contractor has 40 cubic yards of dirt to haul and a budget of $1000, which hauling company should she hire? Explain or show your reasoning.

### Problem 2

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation \(y=118x\), where \(y\) is the number of steps and \(x\) is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps? How many more?

### Problem 3

Find the coordinates of point \(D\) in each diagram:

### Problem 4

Select **all** the pairs of points so that the line between those points has slope \(\frac 2 3\).

\((0,0)\) and \((2,3)\)

\((0,0)\) and \((3,2)\)

\((1,5)\) and \((4,7)\)

\((\text-2,\text-2)\) and \((4,2)\)

\((20,30)\) and \((\text-20,\text-30)\)