2.2 Constant Rates of Change

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Presentation transcript:

2.2 Constant Rates of Change How can you identify and represent proportional relationships?

ADDITIONAL EXAMPLE 1 Randall earns money fixing computers. Is the relationship between the amount Randall earns and the number of days a proportional relationship? Yes; the constant rate of change is $175 per day.

ADDITIONAL EXAMPLE 2 Two pounds of peaches cost $4.50, 5 pounds cost $11.25, and 10 pounds cost $22.50. Show that the relationship between the number of pounds of peaches and the cost is a proportional relationship. Then write an equation for the relationship.

2.2 LESSON QUIZ 7.4.A Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours. 1. Explain how you know whether the relationship between earnings and time is a proportional relationship. Both rates have the same unit rate, $9.25 per hour.

Craig earns extra money as a lifeguard Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours. 2. Identify the constant of proportionality, and write an equation for the proportional relationship. 9.25; If y = earnings and x = hours, = 9.25. 3. Write an equation for the following proportional relationship. = 7.5.

How can you identify and represent proportional relationships? A proportional relationship will have a rate of change that is constant between any two quantities. Find the constant of proportionality, k, and use it to express the relationship as an equation in the form = k.