Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 1 The equation y = 23x describes the approximate number of miles y that a car can go on x gallons of gas.

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Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 1 The equation y = 23x describes the approximate number of miles y that a car can go on x gallons of gas. About how many miles can the car go on 20 gallons of gas? The time y, in seconds, that it takes Joshua to swim x laps is given by y = 11x. Find two solutions to this equation.

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Then/Now You have already used a rate to compare two quantities. (Lesson 5–2) Find rates of change. Solve problems involving rates of change.

Vocabulary rate of change A change in one quantity with respect to another quantity

Example 1 Find Rate of Change from a Graph SCHOOL The graph shows Jared’s quiz scores for the first five weeks after he joined a study group. Find the rate of change from Week 2 to Week 5. change in quiz score change in time  4.3Simplify. Answer:The rate of change in quiz scores is an increase of about 4.3 points per week.

A.A B.B C.C D.D Example 1 A.53.8 B.67.9 C.70.8 D.71.7 SUMMER CAMP The graph shows the number of campers enrolled at a summer camp during its first five years of operation. Find the rate of change from Year 2 to Year 5.

Example 2 Find Rate of Change from a Table DISTANCE The table shows the distance that Amy travels during a week. Find the rate of change. UnderstandYou know the distance Amy travels. You need to find the rate of change. PlanTo find the rate of change, divide the change in distance by the change in time.

Example 2 Find Rate of Change from a Table Answer:The rate of change is 58 mi/day or an increase of 58 miles per day. Solve Miles go from 174 to 406. Time goes from 3 to 7 days. Simplify.

Example 2 Find Rate of Change from a Table CheckUse the rate of change to check the distance Amy travels in 3 days. 3 ● 58 = 174 miles

A.A B.B C.C D.D Example 2 A.15 miles per day B.15 days per mile C.25 miles per day D.25 days per mile The table shows the distance Evie travels in a week. What is the rate of change?

Example 3 Negative Rate of Change COOKIES Natalia is selling cookies. The table shows the relationship between the hours spent selling and the number of cookies that remain. Find the rate of change. Interpret its meaning.

Example 3 Negative Rate of Change Answer:The rate of change is a decrease of 20 cookies per hour. She sells 20 cookies each hour. Simplify.

A.A B.B C.C D.D Example 3 A.an increase of 10 doughnuts per hour B.a decrease of 10 doughnuts per hour C.an increase of 15 doughnuts per hour D.a decrease of 15 doughnuts per hour Joan is selling doughnuts. The table shows the relationship between the hours spent selling and the number of doughnuts that remain. Which answer correctly describes the rate of change of doughnuts over time?

Example 4 Compare Rates of Change INCOME The table shows the yearly incomes of two families. Compare the rates of change.

Example 4 Compare Rates of Change Answer: The income of the King family increases at a faster rate than the income of the Miller family.

A.A B.B C.C D.D Example 4 A.The Brown’s income increases at a faster rate than the Green’s income. B.The Green’s income increases at a faster rate than the Brown’s income. C.The Green’s income decreases at a faster rate than the Brown’s income. D.The incomes of both families increase at the same rate. INCOME The table shows the yearly incomes of two families. Compare the rates of change.

Concept

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