1. Model Direct Variation

2. The Equation of Direct Variation
y = ax
- y varies directly with x
Constant of Variation
- a is called the constant of variation. (Basically, a is slope)
- a cannot be 0.

3. Important: For a relation to be considered a direct variation,
The Relation:
- Must be linear
- Must pass through the origin (O, O) (no intercept)

4. Graph the equation.
y = 3x

5. Graph the equation.
y = -4x

6. Graph the equation.
y = 2x + 1

7. Write and graph a direct variation equation that has the given ordered pair as a solution.
(3, -9)

8. Write and graph a direct variation equation that has the given ordered pair as a solution.
(-7, 4)

9. Write and graph a direct variation equation that has the given ordered pair as a solution.
(5, 3)

10. Write and graph a direct variation equation that has the given ordered pair as a solution.
(6, -2)

11. The variables x and y vary directly
The variables x and y vary directly. Write an equation that relates x and y. Then find y when x = 12.
x = 1, y = 2

12. The variables x and y vary directly
The variables x and y vary directly. Write an equation that relates x and y. Then find y when x = 12.
x = -2, y = 5

13. The variables x and y vary directly
The variables x and y vary directly. Write an equation that relates x and y. Then find y when x = 12.
x = 3, y = -2

14. The variables x and y vary directly
The variables x and y vary directly. Write an equation that relates x and y. Then find x when y = -4.
x = 1, y = 2

15. The variables x and y vary directly
The variables x and y vary directly. Write an equation that relates x and y. Then find x when y = -4.
x = -2, y = 5

16. Tell whether the equation represents direct variation
Tell whether the equation represents direct variation. If so, give the constant of variation.
y = 2x – 1
y = 3x
2x + y = 0
y -1 = 2x
3y = 4x
3y -1 = x