Lesson 1
Understanding Proportional Relationships
Problem 1
Priya jogs at a constant speed. The relationship between her distance and time is shown on the graph. Diego bikes at a constant speed twice as fast as Priya. Sketch a graph showing the relationship between Diego’s distance and time.
![graph. horizontal axis, time in hours, scale 0 to 1, by 1 tenth's. vertical axis, distance in miles, scale 0 to 6, by 2's. line passing through origin and 4 tenths comma 2.](https://cms-im.s3.amazonaws.com/zoLKZcFMiu1uSsCZZcgQNGM5?response-content-disposition=inline%3B%20filename%3D%228-8.3.A1.PP.DiegosmomTask.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A1.PP.DiegosmomTask.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T181831Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6491e19317531beb13d8ccf6a1d9190658a8303ff1e33b1a4e1688769c3b536c)
Solution
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Problem 2
A you-pick blueberry farm offers 6 lbs of blueberries for $16.50.
Sketch a graph of the relationship between cost and pounds of blueberries.
![graph. horizontal axis, blueberries in pounds, scale 0 to 40, by 10's. vertical axis, cost in dollars, scale 0 to 120, by 12's.](https://cms-im.s3.amazonaws.com/dCKue9mkztcZC7nkyFgwKHQB?response-content-disposition=inline%3B%20filename%3D%228-8.3.A1.PP.BlueberriesAxes.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A1.PP.BlueberriesAxes.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T181831Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=eb60ab394bcd7854ebea783332df100f3881d06e0aa76ad81ec0f25dc27ebbe9)
Solution
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Problem 3
A line contains the points \((\text-4,1)\) and \((4,6)\). Decide whether or not each of these points is also on the line:
- \((0,3.5)\)
- \((12,11)\)
- \((80,50)\)
- \((\text-1,2.875)\)
Solution
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(From Unit 2, Lesson 17.)Problem 4
Select all the inequalities that have the same solutions as \(\text-4x<20\).
\(\text-x<5\)
\(4x>\text-20\)
\(4x < \text-20\)
\(x < \text-5\)
\(x>5\)
\(x>\text-5\)
Solution
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(From Unit 4, Lesson 3.)