2. Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and Solve a Direct Variation Equation Example 5Direct Variation Equation

3. Example 2-1a Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Slope formula Simplify. Answer: The constant of variation is 2. The slope is 2.

4. Example 2-1b Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Slope formula Simplify. Answer: The constant of variation is –4. The slope is –4.

5. Example 2-1c Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a. Answer:constant of variation: 4 ; slope: 4

6. Example 2-1d Answer:constant of variation: –3 ; slope: –3 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. b.

7. Example 2-2a 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 containing the points.

8. Example 2-2b Answer:

9. Example 2-3a 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 containing the points.

10. Example 2-3b Answer:

11. Example 2-4a Suppose y varies directly as x, andwhen 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. Example 2-4b Simplify. Answer:Therefore,

13. Example 2-4c Use the direct variation equation to find x when Direct variation equation Answer:Therefore, when Replace y with 15. Divide each side by –3. Simplify.

14. Example 2-4d Suppose y varies directly as x, andwhen a.Write a direct variation equation that relates x and y. b.Use the direct variation equation to find x when Answer: –15 Answer:

15. Example 2-5a 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. WordsThe distance traveled is 330 miles, and the time is 5.5 hours. Variables Distance equals rate times time. Equation 330 mi r5.5h

16. Example 2-5b Solve for the rate. Answer:Therefore, the direct variation equation is Original equation Divide each side by 5.5. Simplify.

17. Example 2-5c Graph the equation. The graph ofpasses through the origin with a slope of 60. Answer:

18. Example 2-5d Estimate how many hours it would take to drive 600 miles. Original equation Replace d with 600. Divide each side by 60. Simplify. Answer:At this rate, it will take 10 hours to drive 600 miles.

19. Example 2-5e Dustin ran a 26-mile marathon in 3.25 hours. a.Write a direct variation equation to find the distance ran for any number of hours. b.Graph the equation. Answer:

20. Example 2-5f c. Estimate how many hours it would take to jog 16 miles. Answer: 2 hours