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Lesson 2 MI/Vocab direct variation constant of variation family of graphs parent graph Write and graph direct variation equations. Solve problems involving.

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Presentation on theme: "Lesson 2 MI/Vocab direct variation constant of variation family of graphs parent graph Write and graph direct variation equations. Solve problems involving."— Presentation transcript:

1 Lesson 2 MI/Vocab direct variation constant of variation family of graphs parent graph Write and graph direct variation equations. Solve problems involving direct variation.

2 Lesson 2 Ex1 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. (x 1, y 1 ) = (0, 0) (x 2, y 2 ) = (1, 2) Answer:The constant of variation is 2. The slope is 2. Slope formula Simplify.

3 Lesson 2 Ex1 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. Answer: The constant of variation is –4. The slope is –4. (x 1, y 1 ) = (0, 0) (x 2, y 2 ) = (1, –4) Slope formula Simplify.

4 A.A B.B C.C D.D Lesson 2 CYP1 A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A.constant of variation: 4; slope: –4 B.constant of variation: 4; slope: 4 C.constant of variation: –4; slope: –4 D.constant of variation: slope:

5 A.A B.B C.C D.D Lesson 2 CYP1 B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A.constant of variation: 3; slope: 3 B.constant of variation: slope: C.constant of variation: 0; slope: 0 D.constant of variation: –3; slope: –3

6 Lesson 2 Ex2 Graph a Direct Variation A.Graph y = x. Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4Draw a line connecting the points.

7 Lesson 2 Ex2 Graph a Direct Variation Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4Draw a line connecting the points. B.

8 Lesson 2 CYP2 1.A 2.B 3.C 4.D A. Graph y = 2x. A.B. C.D.

9 Lesson 2 CYP2 1.A 2.B 3.C 4.D B. A.B. C.D.

10 Lesson 2 CS 1

11 Lesson 2 Ex3 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.

12 Lesson 2 Ex3 Write and Solve a Direct Variation Equation –3 = kSimplify. Answer: Therefore, the direct variation equation is y = –3x.

13 Lesson 2 Ex3 Write and Solve a Direct Variation Equation Answer: Therefore, x = –5 when y = 15. 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.

14 1.A 2.B 3.C 4.D Lesson 2 CYP3 A.y = 3x B.y = 15x C.y = 5x D.y = 45x A. Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y.

15 1.A 2.B 3.C 4.D Lesson 2 CYP3 A.–3 B.9 C.–15 D.–5 B. Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x when y = –45.

16 Lesson 2 Ex4 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. Direct Variation Words Distance equals rate times time. Let r = rate. Variable 330 mi =r × 5.5h Equation

17 Lesson 2 Ex4 Solve for the rate. Answer: Therefore, the direct variation equation is d = 60t. Direct Variation Simplify. Original equation Divide each side by 5.5.

18 Lesson 2 Ex4 B.Graph the equation. The graph of d = 60t passes through the origin with a slope of 60. Answer: Direct Variation

19 Lesson 2 Ex4 C. Estimate how many hours it would take to drive 600 miles. Answer: At this rate, it will take 10 hours to drive 600 miles. Direct Variation Simplify. Replace d with 600. Divide each side by 60. Original equation

20 A.A B.B C.C D.D Lesson 2 CYP4 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. A.d = h B.d = 8h C.d = 8 D.

21 A.A B.B C.C D.D Lesson 2 CYP4 B. Dustin ran a 26-mile marathon in 3.25 hours. Graph the equation. A.B. C.D.

22 A.A B.B C.C D.D Lesson 2 CYP4 C. Estimate how many hours it would take to jog 16 miles. A.1 hour B. C.16 hours D.2 hours

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