Lesson 10

Introducing Graphs of Proportional Relationships

Let’s see how graphs of proportional relationships differ from graphs of other relationships.

Problem 1

Which graphs could represent a proportional relationship? 

Four graphs. 
A:

A

B:

B

C:

C

D:

D

Problem 2

A lemonade recipe calls for \(\frac14\) cup of lemon juice for every cup of water.

  1. Use the table to answer these questions.
    1. What does \(x\) represent?
    2. What does \(y\) represent?
    3. Is there a proportional relationship between \(x\) and \(y\)?
  2. Plot the pairs in the table in a coordinate plane. 
\(x\) \(y\)
1 \(\frac14\)
2 \(\frac12\)
3 \(\frac34\)
4 1

Problem 3

Select all the pieces of information that would tell you \(x\) and \(y\) have a proportional relationship. Let \(y\) represent the distance in meters between a rock and a turtle's current position and \(x\) represent the time in minutes the turtle has been moving.

A:

\(y = 3x\)

B:

After 4 minutes, the turtle has walked 12 feet away from the rock.

C:

The turtle walks for a bit, then stops for a minute before walking again.

D:

The turtle walks away from the rock at a constant rate.

(From Unit 2, Lesson 9.)

Problem 4

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality?

  1. The sizes you can print a photo.

    width of photo (inches) height of photo (inches)
    2 3
    4 6
    5 7
    8 10

  2. The distance from which a lighthouse is visible.

    height of a lighthouse (feet) distance it can be seen (miles)
    20 6
    45 9
    70 11
    95 13
(From Unit 2, Lesson 7.)