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.

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? Direct Variation or not?

Solve for ySolve for y Put the equation in the form y = kx Put the equation in the form y = kx Does y vary directly with x? If so, find k.Does y vary directly with x? If so, find k.

1.1. 2x – 3y = 12x – 3y = 1

2.2. 2x – 3y = 0 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.

• 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= 11/8

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.

X Y

-2 3.2

1 2.4

4 1.6

X Y

4 6

8 12

10 15

XX YY

-2-2 11

22 -1-1

44 -2-2

X Y

-1 2

1 2

2 -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)