# If y varies directly as x and x = 12 when y = 9, find the value of y when x = 32.

###### Question:

## Answers

1)

y = kx

-12 = k(9)

k = -4/3

y = (-4/3)(-4)

y = 16/3

2)

y = kx

8 = 20k

k = 2/5

y = (2/5)(10)

y = 4

3)

y= kx

-6 = k(-14)

k = 3/7

-4 = (3/7)x

-4(7/3) = x

x = -28/3

Linear Functions Unit Test

1. Yes; y=1.625

2. no; y does not vary directly with x

3. Option D

4. Option A

5. 46/1; your car travels 46 miles in 1 hour

6. 1/3

7. -1/3

8. undefined

9. y-3=6(x-8)

10. y+6=-5/8(x+10)

11. y-16=8(x-2)

12. Option A

13. 3x+4y=12

14. y=2x+2

15. perpendicular

16. neither

17. y-3=-3/8(x+2)

18. The functions have the same shape. The y- intercept of y=|x| is 0, and the y- intercept of the second function is -9

19. The two graphs have the same shape but the second graph is shifted 5 units left

20. Option A

21. Option B

22. Positive correlation

These are the answers I put for the short answers

23. You can be confident in your prediction because the more your confident the more you'll have faith in yourself as an individual.

24. y=4.536+0.107*22

0.107*22=2.354

y=4.536+2.254

y=6.89

if rounded y=6.9

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Step-by-step explanation:

So we has to find the direct varition

Step-by-step explanation:

Part A:

Given that

[tex]0.8x=1.6y\Rightarrow x= \frac{1.6}{0.8} y=2y[/tex]

Thus, x = ky where k = 2.

Therefore, the given equation is a direct variation.

Part B:

If y varies directly as x, then y = kx.

Given that y = 5 when x = 2, then

[tex]5=2k \\ \\ \Rightarrow k=\frac{5}{2} =2.5 \\ \\ \Rightarrow y=2.5x[/tex]

When x = 12, y = 2.5(12) = 30.

Part C:

If y varies directly as x, then y = kx.

Given that y = 9 when x = -6, then

[tex]9=-6k \\ \\ \Rightarrow k=-\frac{9}{6} =-\frac{3}{2} \\ \\ \Rightarrow y=-\frac{3}{2}x[/tex]

It can be seen that the equation above satisfies all the rows of the given table, therefore, y varies with x for the data in the question and the equation for the direct variation is [tex]y=-\frac{3}{2}x[/tex]

Part 4:

If y varies directly as x, then y = kx.

Given that y = 1 when x = -2, then

[tex]1=-2k \\ \\ \Rightarrow k=-\frac{1}{2} \\ \\ \Rightarrow y=-\frac{1}{2}x[/tex]

It can be seen that the equation above does not satisfies the other rows of the given table, therefore, y does not vary with x for the data in the question.