1. 2-3 D IRECT V ARIATION Objective: To write and interpret direct variation equations

2. D IRECT V ARIATION A linear function defined by an equation of the form y = kx where k does not equal zero, represents a direct variation. As with any line, k is the slope

3. y = kx The variables are x and y The constant is k

4. For example: If you charge $8 per hour to babysit, how much money will you make? It depends on how many hours you babysit. - so x is the number of hours or the independent variable - and y is the amount you will make or the dependent variable And k is $8 or the constant

5. I DENTIFYING THE D IRECT V ARIATION FROM A T ABLE y = kx So if we want to solve for k, we need to divide each side by x

8. For the following functions, determine whether y varies directly with x. If so, find the constant of variation XY -6-2 31 124 XY -2 34 67 XY -95 3-1 2/3 63 5/8

9. XY -6-2 31 124 Since all three are equal, y varies directly with x, and the constant of variation is 1/3

10. XY -2 34 67 NO XY -95 3-1 2/3 63 5/8 NO

12. F INDING CONSTANT OF VARIATION WHEN GIVEN A DIRECT VARIATION For a direct variation, y = kx Substitute the given (x,y) into the equation to find k Solve for k

13. E XAMPLE For the direct variation, find the constant of variation, and then find the value of y if x=-3. y = -4 when x = 3 y = kx -4 = k(3) -4/3 = k y = -4/3 x y = (-4/3)(-3) y = 4

14. A SSIGNMENT P 74 # 1-22