Lesson 13

Two Graphs for Each Relationship

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

Problem 1

At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for \$5.40.

  1. How much does honey cost per ounce?
  2. How much honey can you buy per dollar?
  3. Write two different equations that represent this situation. Use \(h\) for ounces of honey and \(c\) for cost in dollars.
A blank coordinate plane.
  • Choose one of your equations, and sketch its graph. Be sure to label the axes. 

Problem 2

The point \((3, \frac65)\) lies on the graph representing a proportional relationship. Which of the following points also lie on the same graph? Select all that apply.

A:

$(1, 0.4)$

B:

$(1.5, \frac{6}{10})$

C:

$(\frac65, 3)$

D:

$(4, \frac{11}{5})$

E:

$(15, 6)$

Problem 3

A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, \(r\) (cups), and the amount of peanuts, \(p\) (cups), in this recipe. 

  1. Write the equation for the relationship that has constant of proportionality greater than 1. Graph the relationship.
  2. Write the equation for the relationship that has constant of proportionality less than 1. Graph the relationship.

Problem 4

Here is a graph that represents a proportional relationship.

  1. Come up with a situation that could be represented by this graph.
  2. Label the axes with the quantities in your situation.
  3. Give the graph a title.
  4. Choose a point on the graph. What do the coordinates represent in your situation?
Graph of a line on a coordinate plane, origin O. Horizontal axis has scale 0 to 50 by 5’s. Vertical axis has scale 0 to 100 by 10’s. The line begins at (0 comma 0) and goes through (110 comma 55).
(From Grade7, Unit 2, Lesson 11.)