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://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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T030729Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=49634deeb60156fcfb58c58b8ae4ed35f5f3a84d8328855b8286f71d9f19f261)
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T030729Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e96e89a48deb3aeb650f5280b22b1e69c366502c2ae5ba5742447990e6b9868b)
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
The points \((2,\text-4)\), \((x,y)\), \(A\), and \(B\) all lie on the line. Find an equation relating \(x\) and \(y\).
![graph. horizontal axis, scale 0 to 11, by 1's. vertical axis, scale -5 to 3, by 1's.](https://cms-im.s3.amazonaws.com/CCi99rTZFMggsJnqYDfFBtKU?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.06.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=20240727T030729Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a51e63c13392ef9abf5e58cae56bed9096159cebd61d4c72e8575864f0222c1b)