Question

For questions 1-3

Determine whether the equation represents a direct variation. If it does, find the constant of variation.

1. 2 y = 5x +1
a. Not a direct variation
b. Direct variation, constant of variation is 5/2
c. Direct variation, constant of variation is 2/5
d. Direct variation, constant of variation is 1 -2/5

2. -12x = 6y
a. Not a direct variation
b. Direct variation, constant of variation is 1/2
c. Direct variation, constant of variation is 2
d. Direct variation, constant of variation is -2

3. .7x -1.4y = 0
a. Not a direct variation
b. Direct variation, constant variation is 1/2
c. Direct variation, constant variation is 2
d. Direct variation, constant variation is -2

For questions 4-6
Suppose y varies directly with x. Write a direct variation equation that relates x and y.

4. y= -10 when x =2
a. y= -5x
b. y= -1/5x
c. y= 5x
d. y= 1/5 x

5. y= 7 1/2 when x=3
a. y= 3/2x
b. y= 2/3x
c. y= 5/2
d. y= 2/5
6. y=10.4 when x=4
a. y= 3.4x
b. y= 3.8x
c. y= 3.2x
d. y= 2.6x

For questions 7 and 8
For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.

7. (x.y)
(3, 5.4)
(7, 12.6)
(12, 21.6)

a. Not a direct variation
b. Direct variation, y= 1.8x
c. Direct variation, y= 4x
d. Direct variation, y= 5/9x

8. (x,y)
(-2,1)
(3,6)
(8,11)

a. Not a direction variation
b. Direct variation, y=x
c. Direct variation, y=2x
d. Direct variation, y= -2x

Answer 1

Number 2 is D. The pattern is quite simple, basically the formula for direct variation is y=kx, so in number 2 the problem shows -12x=6y, so then you would end up dividing the numbers, and this should you solve your other answers.
Hope this helps!

Answer 2

1. A - Not a Direct Variation

2. D - Direct Variation, Constant of Variation is -2

3. B - Direct Variation, Constant of Variation is 1/2

4. A - y = -5x

5. C - y = 5/2x

6. D - y = 2.6x

I'm not sure about your 7 and 8 because I don't have them. I'm sorry! But here ya'll go