1. 9-1 Notes

2. Direct Variation: Two variables, y and x, vary directly if: y = If k is any nonzero constant. Example: The equation: y = 5x exhibits direct variation because:

3.  Inverse Variation: Two variables, x and y, vary inversely if:y = for any nonzero constant, k Example: y = 5/x exhibits inverse variation because:

4.  Joint Variation: Three variables, x, y, and z vary jointly if: z = for any non-zero constant, k. Example: z = 5xy exhibits joint variation because:

5. Determine if the following exhibit direct or inverse variation: a. xy = 10b. y = x – 1c. x = 5y

6.  Determine if the following equations exhibit direct variation, inverse variation, or neither: a. 2y = x – 1 b. 5y = 2x

7.  The variables x and y vary inversely, and y – 8 when x = 3.  a. Write an equation that relates x and y:  b. Use your equation from part a. to find y when x = -4

8.  Determine whether x and y show direct variation, inverse variation, or neither in the following tables: xyxyxy 1.520336530 2.5127105742 47.55501166 56164820120 74.3214027162 103401732192 152518 306

9.  The variable z varies jointly with x and y. Use the given values to write and equation relating x, y, and z: x = 1, y = 1/3, and z = 5

10.  The variable z varies jointly with x and y. Use the given values to write and equation relating x, y, and z:  x = 5/6, y = 3/10, and z = 8

11. Write an equation for the given relationship: X varies inverssely with y and directly with z:

12. Write an equation for the given relationship: m varies inversely with a and jointly with b and c:

13.  Section 9-1: Page 537, # 22-46 even, and 54