1. 8-1/2-2 DIRECT AND INVERSE VARIATION

2. Direct Variation Equation: y = kx Solve for constant “k” k = y/x As x increases, y increases As x decreases, y decreases Inverse Variation Equation: y = k/x Solve for constant “k” k = xy As x increases, y decreases As x decreases, y increases

3. EX 1) DETERMINE WHETHER Y VARIES DIRECTLY OR INDIRECTLY WITH X. IF SO, FIND THE CONSTANT Question a. b. c. Answers Indirect, k =10 Neither Direct, k = 2

4. EX 2) DETERMINE WHETHER Y VARIES DIRECTLY OR INDIRECTLY WITH X. IF SO, WRITE THE EQUATION. xy 215 47.5 103 152 Inverse? Check constant k = xy =30 Yes! y = 30/x xy 0.28 0.520 1.040 1.560 Direct? Check constant k = y/x =40 Yes! y = 40x xy 210 48 3 151.5 Inverse? Check constant k = xy =20 =32 =30 =22.5 No! Neither y = k/x y = kx

5. EX 3) WRITE A DIRECT VARIATION THAT PASSES THROUGH EACH POINT a. (5,4)  b.(8,-3) Find constant k = y/x Plug into equation y = kx

6. EX 4) WRITE AN INVERSE VARIATION THAT PASSES THROUGH EACH POINT a. (7, 11) b. (-3, -6) y = k/x Find constant k = xy Plug into equation y = k/x

7. EX 5) a)Suppose y varies directly with x and y = 9 when x = -15. Write an equation and find what y is when x = 21. Find constant: k = y/x = 9/-15 = -3/5 Write Equation: y = kx = y = (-3/5)x When x = 21, then y = kx = y = (-3/5)(21) y = -63/5 Find constant k = y/x Plug into equation y = kx

8. EX 5) b) Suppose y varies inversely with x and x = 4 when y = 12. Write an equation and find what y is when x = 10. Find constant: k = xy = 4(12) = 48 Write Equation: y = k/x = y = 48/x When x = 10, then y = k/x = y = 48/10 y = 24/5 Find constant k = xy Plug into equation y = k/x

9. EX 5 CONTINUED - T.O.O. c) Suppose y varies directly with x and y = 15 when x = 3. Write an equation and find what y is when x = 12. d) Suppose y varies inversely with x and x = 8 when y = -7. Write an equation and find what y is when x = 2. Answers c) y = 5x; If x = 12, then y = 60 d) y = -56/x; If x = 2, then y = -28 Find constant k = y/x Plug into equation y = kx Find constant k = xy Plug into equation y = k/x

10. 3 VARIABLES EX 6) Suppose z varies directly with x and inversely with y and that z = 15 when x = 6 and y = 2. Write an equation and determine what z is when x = 4 and y = 9. Find k. Write equation. Find z.

11. EX7) T.O.O 1)Suppose z varies inversely with the (product of x and y) and z = 0.5 when x = 2 and y = 4. Write an equation and find what z is when x = 4 and y = 9. 2)Write a direct variation for (-2,3) and use it to find the missing coordinate of (x,6). 3)Write an inverse variation for (-2,3) and use it to find the missing coordinate of (x,6). Answers 1)z = 4/(xy), z = 1/9 2)y = (-3/2)x, x = -4 3)y = -6/x, x = -1

12. HOMEWORK W-S 8-1/2-2

13. TOD Given (3, 5) find BOTH the direct and indirect variation. Then, solve both equations use x=-9 and solve for x. Direct variation equation Direct variation answer -15 Indirect variation equation Indirect variation answer -5/3