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2-3 Direct Variations. Direct Variation: y = kx y varies directly with x y varies directly as x k = constant of variation = slope The graph of a direct.

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Presentation on theme: "2-3 Direct Variations. Direct Variation: y = kx y varies directly with x y varies directly as x k = constant of variation = slope The graph of a direct."— Presentation transcript:

1 2-3 Direct Variations

2 Direct Variation: y = kx y varies directly with x y varies directly as x k = constant of variation = slope The graph of a direct variation ALWAYS goes through (0,0), the origin K is never 0. K can be positive or negative.

3 Direct Variation or not?  Solve for y  Put the equation in the form y = kx  Does y vary directly with x? If so, find k. 1. 2x – 3y = x – 3y = 0

4 3. ½ x + 1/3y = y = 2x 5. 3y + 4x = 8

5 Write and solve a direct variation Use the given x and y values to find k. Rewrite your equation with the value for k and the x and y variables.

6 Suppose y varies directly as x, and y = 9 when x = -3. Use the direct variation equation to find x when y = 15. Write a Direct Variation Equation

7  If y = 2 2 / 3 when x = ¼,find y when  x= 1 1 / 8  If y =4 when x =12, find y when x = -24

8 Data Tables y = kx also equals y/x = k If k (constant of variation) is the same for each y divided by x, then you have a direct variation.

9 Determine if each data table represents a direct variation. If so, write the equation. XY

10 XY

11 XY

12 XY

13 Write the direct variation equation that goes through each point. Use (x,y) in y=kx. Find k, write your equation. 1) (1,2) 2) ( -3, 14)


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