Lesson 4
Comparing 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.
![graph, horizontal axis, dirt in cubic yards, scale 0 to 6, by 1's. vertical axis, cost in dollars, scale 0 to 55, by 5's. line passing through origin, 1 comma 25 and 2 comma 50.](https://cms-im.s3.amazonaws.com/2RkK2SGArYJgYNgMezguwLY8?response-content-disposition=inline%3B%20filename%3D%228-8.3.A3.dirtgraph.2.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A3.dirtgraph.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004413Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8be524600b772b84c35e1472f872a4426755cd361901ceba6291664c9ea5b0d3)
- 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.
Solution
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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?
Solution
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Problem 3
Find the coordinates of point \(D\) in each diagram:
![xy plane with no grid. right triangle with vertices at -6 comma 0, 2 comma 10, and 2 comma 0. hypotenuse crosses y axis at D.](https://cms-im.s3.amazonaws.com/8iQvRy5dXTDE6jDYAeTiQDGA?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004413Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=76fdeda860783b37d938ae8a0b4581c2e51582f7b0763022ca9b7302250240a4)
![xy plane with no grid. right triangle with vertices at -4 comma 3, 2 comma 7, and 2 comma 3. hypotenuse crosses y axis at D.](https://cms-im.s3.amazonaws.com/HW84Na6KqSj8MyRE25zRQoAR?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.01.1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.01.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004413Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=541274f57bbc264d47177d6a939c409f3241c4ad4cd26b3e63edc0e259cadab3)
Solution
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(From Unit 2, Lesson 11.)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 \((\text-20,\text-30)\)
Solution
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(From Unit 2, Lesson 11.)