Question

⦁ Determine if the equation represents a direct variation. .8x = 1.6y ⦁ Suppose y varies directly with x. Write a direction variation equation that relates x and y. Then find the value of y when x = 12. y=5 when x=2. ⦁ For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y -6 9 1 -1.5 8 -12 ⦁ For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y -2 1 3 6 8 11

Answer 1

Part A:

Given that 

$0.8x=1.6y\Rightarrow x= \frac{1.6}{0.8} y=2y$

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

$5=2k \\ \\ \Rightarrow k=\frac{5}{2} =2.5 \\ \\ \Rightarrow y=2.5x$

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

$9=-6k \\ \\ \Rightarrow k=-\frac{9}{6} =-\frac{3}{2} \\ \\ \Rightarrow y=-\frac{3}{2}x$

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 $y=-\frac{3}{2}x$



Part 4:

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

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

$1=-2k \\ \\ \Rightarrow k=-\frac{1}{2} \\ \\ \Rightarrow y=-\frac{1}{2}x$

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.

Answer 2

Answer: 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