Lesson 1
Understanding Proportional Relationships
Let’s study some graphs.
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141541Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7da8d304130feb84e25232b13a30c723931f2b0a8660a8e7c1651cb852a22788)
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141541Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=74e3a18129a4f038540296dd74ce04f1caf09bf2b65c1dbe0b702c2236d276ff)
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:
- \((0,3.5)\)
- \((12,11)\)
- \((80,50)\)
- \((\text-1,2.875)\)
Problem 4
Select all the inequalities that have the same solutions as \(\text-4x<20\).
A:
\(\text-x<5\)
B:
\(4x>\text-20\)
C:
\(4x < \text-20\)
D:
\(x < \text-5\)
E:
\(x>5\)
F:
(From Unit 4, Lesson 3.)
\(x>\text-5\)