Lesson 10

Introducing Graphs of Proportional Relationships

Problem 1

Which graphs could represent a proportional relationship?

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.

Solution

(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