1. 5.2 Slope and Direct Variation What you’ll learn: 1.Write and graph direct variation equations. 2.To solve problems involving direct variation.

2. Direct Variation Direct Variation – described by an equation of the form y=kx where k  0. Read “y varies directly as x.” In the equation y=kx, k is the constant of variation. (it is also the slope) To graph a direct variation equation, they will start at the origin and rise and run based on the k or slope.

3. Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points. 1. k=4m=4 2. k=-⅔ m=-⅔ 3. k=⅓m=⅓

4. Graph each direct variation equation 1.y=-⅔x 2.y=3x 3.y=-¾x

5. Writing and solving direct variation equations. 1.Find k (plug in x and y to find k) 2.Use the k and the x or y that you are given to find the other value. Ex:If y varies directly as x and y=9 when x=-3, find x when y=15. y=kx 9=-3k k=-3Equation: y=-3x 15=-3x-5=x

6. Write a direct variation equation. Then solve. 1.If y varies directly as x and y=-20 when x=10, find x when y=48. y=kx20=-10kk=-2 y=-2x 48=-2x-24=x 2.If y varies directly as x and y=-24 when x=-6, find y when x=10. y=kx-24=-6kk=4y=4x y=4(10)y=40

7. Classwork p. 267 4-11 all 15-42 all