# Direct and Inverse Variations - PowerPoint PPT Presentation

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## Direct and Inverse Variations

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### Direct and Inverse Variations Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or ... – PowerPoint PPT presentation

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Title: Direct and Inverse Variations

1
Direct and InverseVariations
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 2.4 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
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
• Lets do another.
• If y varies directly with x and y 12 when x
2, find y when x 8.

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

11
Direct Variation
• Cross multiply 96 2y
• Solve for y. 48 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 xs and ys.
• In Inverse variation we will Multiply them.
• x1y1 x2y2

14
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

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