Lesson 12

Using Graphs to Compare Relationships

The practice problem answers are available at one of our IM Certified Partners

Problem 1

The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

__________________ vs volume

Graph of points on coordinate plane, origin O. 

_____________________ vs volume

Graph of points on coordinate plane, origin O.
  1. Which graph is which? Give them the correct titles.
  2. Which quantities appear to be in a proportional relationship? Explain how you know.
  3. For the proportional relationship, find the constant of proportionality. What does that number mean?

Problem 2

Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. 

  1. Draw a graph with two lines that represent the bike rides of Lin and Andre. 
  2. For each line, highlight the point with coordinates \((1,k)\) and find \(k\).
  3. Who was biking faster?

Problem 3

Match each equation to its graph.

  1. \(y = 2x\)
  2. \(y = \frac45 x\)
  3. \(y = \frac14 x\)
  4. \(y = \frac23 x\)
  5. \(y = \frac43 x\)
  6. \(y = \frac32 x\)

1

Graph of a linear function, origin O.

2

Graph of a linear function, origin O. 

3

Graph of a linear function, origin \(O\). 

4

Graph of a linear function, origin O. 

5

Graph of a linear function, origin O. 

6

Graph of a linear function, origin O.