1. NOTES 2.3 & 9.1 Direct and Inverse Variation

2. Direct Variation A function in the form y = kx, where k is not 0 Constant of variation (k) is the coefficient of x. x and y are said to vary directly with each other.

3. Is an equation a direct variation? Solve for y. Does it fit the form y = kx? Examples: 1. 2y = 5x + 1 2. -12x = 6y

4. Writing an Equation Given x and y 1. Use k = to find the constant of variation 2. Write the new direct variation function. Examples 3. (5, 1) 4. x = -5, and y = -10

5. Using a Proportion Find the missing value for the direct variation. 5. If y = 4 when x = 3, find y when x = 6. 6. If y = 10 when x = -3, find x when y = 2.

6. Direct Variations and Tables xy -23.2 12.4 41.6 xy46 812 1015 7. 8. Tell whether y varies directly with x. If it does, write an equation for the direct variation.

7. Inverse Variation An equation in the form xy = k or y =, where k is not 0 Constant of variation (k) is the product of x and y for an ordered pair (x, y) Suppose y varies inversely with x and y = 9 when x = 2. Write an equation for the inverse variation.

8. Is the relationship between the values in each table a direct variation, inverse variation, or neither? Is the relationship between the values in each table a direct variation, inverse variation, or neither? 11.12. 13. xy 23.2 41.6 61.1xy1.218 1.421 1.624 xy0.80.9 0.61.2 0.41.8