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:
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. 1. 2x – 3y = x – 3y = 0
3. ½ x + 1/3y = y = 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.
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
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
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. If so, write the equation. XY
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)