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. 

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.  

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:

  1. \((0,3.5)\)
  2. \((12,11)\)
  3. \((80,50)\)
  4. \((\text-1,2.875)\)
(From Unit 2, Lesson 12.)

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.
(From Unit 2, Lesson 11.)