Proportional and Nonproportional Situations

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Presentation transcript:

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

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

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

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

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.

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

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.

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.

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 …

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