Question

Y varies directly with x Part 2

22. If y = 5 when x = -3, find x when y = -1
23. If y = -7 when x = -3, find y when x = 9
24. If y = 25 when x = 15, find y when x = 6

Answer 1

Problem 22

Answer: x = 3/5

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Step-by-step explanation:

y = kx is the general form for direct variation. K is some constant.

Plug in (x,y) = (-3,5) to find k

y = kx

5 = k*(-3)

-5/3 = k

k = -5/3

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The equation is y = (-5/3)x. Now plug in y = -1 to find x

y = (-5/3)x

-1 = (-5/3)x

(-5/3)x = -1

x = -1*(-3/5)

x = 3/5

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Problem 23

Answer: y = 21

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Step-by-step explanation:

Same idea as above. First we need to find k.

y = kx

-7 = k(-3) .... plug in x = -3 and y = -7

-3k = -7

k = 7/3

The equation is y = (7/3)x

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We can use this to find y when x = 9

y = (7/3)x

y = (7/3)*9 .... plug in x = 9

y = 21

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Problem 24

Answer: y = 10

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Step-by-step explanation:

First find k

y = kx

25 = k*15

25/15 = k

5/3 = k

k = 5/3

The equation is y = (5/3)x

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Now find y when x = 6

y = (5/3)x

y = (5/3)*6

y = 10

Answer 2

22. 3/5

23. 21

24. 10

Step-by-step explanation:

In each case, multiply the old value of the variable of interest by the new/old ratio of the given variable values.

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22. x = (-1/5)(-3) = 3/5

23. y = (9/-3)(-7) = 21

24. y = (6/15)(25) = 10

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The proportions can be written as either of ...

newX/newY = oldX/oldY ⇒ newX = (newY/oldY)(oldX)

or, the same thing with x and y interchanged:

newY/newX = oldY/oldX ⇒ newY = (newX/oldX)(oldY)