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