1. Direct and Inverse Variation
Algebra I

2. Direct Variation When the line passes through the origin.
When y increases, x increases.
Equation: y = kx, where k 0.
Constant of variation – k
Say “ y varies directly with x”

3. Identifying the constant of variation
y = 6x 6 is the constant of variation (k) These can be graphed on the calculator using ‘y=‘ button, to see what the graph should look like.

4. Examples:
y = 28, x = find x when y = 52

5. Examples:
y = 28, x = 7 find x when y = 52 y = kx y = kx

6. Examples:
y = 28, x = 7 find x when y = 52 y = kx y = kx 28 = k(7) 52 = 4x = k 13 = x y = 4x

7. Example:
y = 27, x = find x when y = 45

8. Example:
y = 27, x = 6 find x when y = = k(6) 45 = 9/2x 6 6 (2/9)45 = x 9/2 = k 10 = x Y = 9/2x

9. Example:
y = -7, x = find y when x = 20

10. Example:
y = -7, x = -14 find y when x = = k(-14) y = (½) y = 10 ½ = k y = ½x

11. Inverse (Indirect) Variation
Line going away from the origin.
When one value (x or y) increases, the other value (x or y) decreases.
Equation xy = k
Say “y varies inversely as x” or “y is inversely proportional to x”.

12. Different forms of the equation
xy = k Y = k/x or x = k/y

13. Example:
If y = 12 when x = 5, find y when x = 3 xy = k 3y = 60 (5)(12) = k = k y = 20 xy = 60

14. Example: If y = 7, when x = -2; find y when x = 7
If y = 8.5, when x = -1; find x when y = -1
If y = 8, when x = 1.55; find x when y = -0.62

15. Example: If y = 7, when x = -2; find y when x = 7 xy = -14 y = -2
If y = 8.5, when x = -1; find x when y = -1
xy = x = 8.5
If y = 8, when x = 1.55; find x when y = -0.62
xy = x = -20