1. Proportional and Nonproportional Situations
4.4
Proportional and Nonproportional Situations
How can you distinguish between proportional and nonproportional situations?

2. ADDITIONAL EXAMPLE 1
The graph shows the water level as a bathtub fills. Does the graph show a linear relationship? Is the relationship proportional or nonproportional?
yes; nonproportional

3. ADDITIONAL EXAMPLE 2
The change in a test score for each incorrect answer is represented by the equation y = , where x is the number of incorrect answers. Is the relationship between the number of incorrect answers and the change in score proportional or nonproportional?
proportional

4. ADDITIONAL EXAMPLE 3
The table shows the distance of a train from a station and the time it will take to arrive. The relationship is linear. Is it proportional or nonproportional?
nonproportional

5. ADDITIONAL EXAMPLE 4 A
John has a choice of hiring two plumbers. In both cases, x is the number of hours and y is the total charge in dollars. Compare and contrast these two situations.
Plumber A: y = 75x
Plumber B:
Plumber A’s charges are a proportional relationship; Plumber B’s charges are not. Plumber B charges an initial fee of $100 and a lower hourly rate.

6. 4.4 LESSON QUIZ
8.5.F
Explain whether each shows a proportional relationship. 1.
No; the graph does not go through the origin.

7. Explain whether each shows a proportional relationship.2.
Yes; the ratio of y to x is constant. 3.
12x = 5y
Yes; the equation can be written in the form y = mx + b, and b = 0.

8. 4.
Compare and contrast.
The cost without a discount card is proportional, with a discount card it is not. The cost is more expensive with the discount card initially, but the per-case rate without it is more expensive.

9. A geometric progression is a sequence or list of numbers with a common ratio r between the terms. One geometric progression is a sequence with a common ratio of 2: 1, 2, 4, 8, 16, 32 …

10. How can you distinguish between proportional and nonproportional situations?
Sample answer:
Determine whether the relationship is linear and the y-intercept is 0.