Then/Now You found rates of change of linear functions. (Lesson 3–3) Write and graph direct variation equations. Solve problems involving direct variation.

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Presentation transcript:

Then/Now You found rates of change of linear functions. (Lesson 3–3) Write and graph direct variation equations. Solve problems involving direct variation.

Vocabulary direct variation: an equation of the form y=kx where k ≠ 0 constant of variation: k is the constant of variation or the constant ratio of y:x constant of proportionality: same as the constant of variation

Example 1 A Slope and Constant of Variation A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

Example 1 B Slope and Constant of Variation B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

A.A B.B C.C D.D Example 1 CYP A A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

A.A B.B C.C D.D Example 1 CYP B B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

Example 2 Graph a Direct Variation

A.A B.B C.C D.D Example 2 CYP Graph y = 2x.

Concept

Example 3 A Write and Solve a Direct Variation Equation A. Suppose y varies directly as x, and y = 9 when x = –3. Write a direct variation equation that relates x and y. Find the value of k. Direct variation formula Replace y with 9 and x with –3. Divide each side by –3. –3 = kSimplify.

Example 3 A Answer: Therefore, the direct variation equation is y = –3x. Write and Solve a Direct Variation Equation

Example 3 B B. Use the direct variation equation to find x when y = 15. Simplify. Direct variation equation Replace y with 15. Divide each side by –3. Write and Solve a Direct Variation Equation

A.A B.B C.C D.D Example 3 CYP A A. Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y.

A.A B.B C.C D.D Example 3 CYP B B. Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x when y = –45.

Example 4 A Estimate Using Direct Variation A. TRAVEL The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. Write a direct variation equation to find the distance driven for any number of hours.

Example 4 B Estimate Using Direct Variation B.Graph the equation. The graph of d = 60t passes through the origin with a slope of 60. Answer:

Example 4 C Estimate Using Direct Variation C. Estimate how many hours it would take to drive 500 miles.

A.A B.B C.C D.D Example 4 CYP A A. Dustin ran a 26-mile marathon in 3.25 hours. Write a direct variation equation to find the distance run for any number of hours.