1. Direct Variation Rhonda Yost

2. What is Direct Variation? A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation. As with any line, the slope k is constant. When x and y are variables, you can write k = y/x, so the ratio y : x equals the constant k, the constant of variation.

3. Is this an example of direct variation? XY 28 312 520 Use the equation k = y/x to solve for k. Then write it in the form y = kx. y/x = 8/2 = 12/3 = 20/5 = 4, so y varies directly with x. The constant of variation is 4. The equation is y = 4x.

4. Is this an example of direct variation? XY 14 27 516 Use the equation k = y/x to solve for k. Then write it in the form y = kx. Since 4/1, 7/2, and 16/5 are not equal, y/x is not constant. y does not vary directly with x.

5. Is this an example of direct variation? XY -6-2 31 124 Use the equation k = y/x to solve for k. Then write it in the form y = kx. y/x = -2/-6 = 1/3 = 4/12 = 1/3, so y varies directly with x. The constant of variation is 1/3. The equation is y = 1/3x.

6. Is this an example of direct variation? Use the equation k = y/x to solve for k. Then write it in the form y = kx. XY -2 34 67 Since -2/-1, 4/3, and 7/6 are not equal, y/x is not constant. y does not vary directly with x.

7. Is this an example of direct variation? Use the equation k = y/x to solve for k. Then write it in the form y = kx. XY -95 3-1 2/3 63 5/8 Since 5/-9 = (-1 2/3)/3, but does not equal (3 5/8)/6, y/x is not constant. y does not vary directly with x. A short cut to answering this would be that the answer to the first two problems is a negative number, but the third is positive, therefore they are not all equal.

8. Test Prep Which equation does NOT represent a direct variation? A.y – 3x = 0 B.y + 2 = ½ x C.y/x = 2/3 D.Y = x/17 The correct answer is B because it cannot be written in the form y = kx

9. Water Conservation A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water varies directly with the amount of time the faucet drips. a.Find the constant of variation k and write an equation to model the direct variation  Water wasted varies directly with time, therefore let water wasted be y and time in minutes be x.  Substitute 1 for y and 3 for x  1 = k (3)  Solve for k  1/3 = k  The constant of variation k is 1/3. the equation y = 1/3x models the direct variation. b.Find how long the faucet must drip to waste 4.5 cups of water.  Substitute 4.5 for y into your direct variation formula  4.5 = 1/3x  Solve for x  (4.5)(3) = x  Simplify  x = 13.5  The faucet must drip for 13.5 minutes to waste 4.5 cups of water.

10. Homework pg. 75 Exercises 24-27 Y varies directly with x 24. If y = 4 when x = -2, find x when y = 6. 25. If y = 6 when x = 2, find x when y = 12 26. If y = 7 when x = 2, find y when x = 3 27. If y= 5 when x= -3, find y when x = -1 If you are done early work on exercises 41-45