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.
2x – 3y = 1
2x – 3y = 0

4. 3. ½ x + 1/3y = 0
4. 7y = 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. 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.

7. If y = 2 2/3 when x = ¼ ,find y when
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
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

10. X Y 4 6 8 12 10 15

11. X Y -2 1 2 -1 4

12. X Y -1 2 1 -4

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)