1. Reassessments and Make-ups
Grade Distribution
3rd
6th
7th A 3 2 B 9 13 10 C 7 6 D 5 F
No Show 4
Avg.
81.25
78.93
79.95
Reassessments and Make-ups
due Thursday, Feb 5th
12/1/2018 2:31 AM
4.6: Direct Variations
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2. Direct and Inverse Variations
Section 8-1
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4.6: Direct Variations

3. Direct Variation
A. Direct Variation: A linear function which two variables are which one is a constant multiple of the other; when one variable changes the other changes in proportion to the first y x
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4.6: Direct Variations

4. Direct Variation B. Direct Variation:
K = Constant of Variation or SLOPE
There is NO y-intercept
X = Independent Variable
Y = Dependent Variable
If X goes up, Y has to go up.
If X goes down, Y has to go down.
C. KEYWORD: VARY(ies) DIRECTLY or DIRECTLY PROPORTIONAL
Divide the variables
Y varies directly with X
k is not always going to be used in all questions
It is used only when the problem is comparing itself
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4.6: Direct Variations

5. Example 1
Tell whether the equation, 2x – 3y = 0 represents direct variation. Identify the constant of variation.
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4.6: Direct Variations

6. Example 2
Tell whether the equation, 2x + y = 3 represents direct variation. Identify the constant of variation.
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4.6: Direct Variations

7. Your Turn
Tell whether the equation, 3x + 8y = 0 represents direct variation. Identify the constant of variation.
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4.6: Direct Variations

8. Example 3
The weekly salary a woman earns, S, varies directly as the number of hours, h, which she works.  Express this relation as a formula.
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4.6: Direct Variations

9. Example 4
The resistance R, of a copper wire, varies directly as its length L.  Write this relation as a formula using k as the constant of variation.
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4.6: Direct Variations

10. Your Turn
At a recycling center, computers and computer accessories can be recycled for a fee f based on weight, w.  Write this relation as a formula using k as the constant of variation.
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4.6: Direct Variations

11. Example 5
Would this situation be a direct variation? Your weekly pay, p, is directly proportional to the number of hours, h, she works at the record store.
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4.6: Direct Variations

12. Example 6
Would this situation be a direct variation? If the area (A) of a rectangle remains constant and the width (w) decreases.
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4.6: Direct Variations

13. Your Turn
Would this situation be a direct variation? If the temperature is constant, the pressure of a gas (P) in a container varies inversely as the volume of the container (V).
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4.6: Direct Variations

14. Example 7
If a varies directly as b and a = 3 when b = 24, find b when a = 10.
Would k be necessary into this equation?
Another way of finding out this problem is through proportions.
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4.6: Direct Variations

15. Example 8
If y varies directly with x. If y = 4 when x = 2, find y when x = –6.
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4.6: Direct Variations

16. Example 9
If y varies directly as x2 and y = 64 when x = 2, find y when x = 8.
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4.6: Direct Variations

17. Your Turn
If y varies directly with x. If y = 75 when x =25, find x when y = 25.
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4.6: Direct Variations

18. Assignment
Worksheet
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4.6: Direct Variations

19. 8-1: Direct and Inverse Variations
Example 3
The values of y and x vary directly. Determine the constant variation if x = 3 when y = 12.
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4.6: Direct Variations
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8-1: Direct and Inverse Variations 19

20. 12/1/2018 2:31 AM
4.6: Direct Variations