1. Direct and Inverse Variations

2. Direct Variation
When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

3. Direct Variation
Direct variation uses the following formula:

4. Direct Variation example:
if y varies directly as x and y = 10 as x = 2.4, find x when y =15.
what x and y go together?

5. Direct Variation
If y varies directly as x and y = 10 find x when y =15.
y = 10, x = make these y1 and x1
y = 15, and x = ? make these y2 and x2

6. Direct Variation
if y varies directly as x and y = 10 as x = 2.4, find x when y =15

7. How do we solve this? Cross multiply and set equal.
Direct Variation
How do we solve this? Cross multiply and set equal.

8. Direct Variation We get: 10x = 36
Solve for x by diving both sides by 10.
We get x = 3.6

9. Direct Variation Let’s do another.
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Set up your equation.

10. If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Direct Variation
If y varies directly with x and y = 12 when x = 2, find y when x = 8.

11. Cross multiply: 96 = 2y Solve for y. 48 = y.
Direct Variation
Cross multiply: 96 = 2y
Solve for y = y.

12. Inverse Variation
Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.

13. Inverse Variation With Direct variation we Divide our x’s and y’s.
In Inverse variation we will Multiply them.
x1y1 = x2y2

14. Inverse Variation x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3
If y varies inversely with x and y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y = 3

15. Inverse Variation
If y varies inversely as x and x = 18 when y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 13.5