Answer :
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.
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.
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