Direct and InverseVariations

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.

Direct Variation

Direct variation uses the following formula

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?

Direct Variation

- If y varies directly as x and y 10 find x when

y 15. - y 10, x 2.4 make these y1 and x1
- y 15, and x ? make these y2 and x2

Direct Variation

- if y varies directly as x and y 10 as x 2.4,

find x when y 15

Direct Variation

- How do we solve this? Cross multiply and set

equal.

Direct Variation

- We get 10x 36
- Solve for x by diving both sides by 10.
- We get x 3.6

Direct Variation

- Lets do another.
- If y varies directly with x and y 12 when x

2, find y when x 8. - Set up your equation.

Direct Variation

- If y varies directly with x and y 12 when x

2, find y when x 8.

Direct Variation

- Cross multiply 96 2y
- Solve for y. 48 y.

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.

Inverse Variation

- With Direct variation we Divide our xs and ys.
- In Inverse variation we will Multiply them.
- x1y1 x2y2

Inverse Variation

- 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

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