1. Slope and Direct Variation Lesson 5-2

2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is the ______________________. (k is always equal to the __________________.) Direct variation is also known as a direct __________________________. Direct variation y = kx k constant of variation slope proportion

3. 1 up 1 right 1 A direct variation will ALWAYS pass through the origin.

4. Graph y = 2x m = _______ Remember, the first point will always be (0,0) in a direct variation. Find additional points using the slope.

5. up 3 left 2

6. Moving up 2 and left 3 will fall on the same line as moving down 2 and right 3.

9. y = kx 9 -3 9 = k (-3) -3 = k y = -3x 15 = -3x -5 = x

10. y = kx 15 = k(5) 15/5 = 5k/5 3 = k y = 3x -45 = 3x -45/3 = (3x)/3 -15= x

11. Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve. 7. If y = 27 when x = 6, 8.If y = 10 when x = 9, find x when y = 45. find x when y = 9. ________________________ ____________________ ________________________ ___________________ ________________________ ______________________ ________________________ ______________________

12. Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve. 9. If y = -7 when x = 14, 10. find y when x = 20. ________________________ ______________________ ________________________ ______________________

13. Using Direct Variations to Solve Problems The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. A. Write a direct variation equation to find the distance driven for any number of hours. y = 60 x 10 hours

14. A flock of geese migrated 375 miles in 7.5 hours. A. Write a direct variation equation to find the distance flown in any time. y = 50 x B.Estimate how many hours of flying time it would take the geese to migrate 3000 miles. y = distance, x = time in hours y = 50 x 3000 = 50 x 60 hours = x