2-3 Direct Variations.

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Presentation transcript:

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 variation ALWAYS goes through (0,0), the origin K is never 0. K can be positive or negative.

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. 2x – 3y = 1 2x – 3y = 0

3. ½ x + 1/3y = 0 4. 7y = 2x 5. 3y + 4x = 8

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.

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

If y = 2 2/3 when x = ¼ ,find y when If y =4 when x =12, find y when x = -24

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.

Determine if each data table represents a direct variation Determine if each data table represents a direct variation. If so, write the equation. X Y -2 3.2 1 2.4 4 1.6

X Y 4 6 8 12 10 15

X Y -2 1 2 -1 4

X Y -1 2 1 -4

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)