Question

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?

A. y = –4/3x
B. y = –3/4x
C. y = 3/4x
D. y = 4/3x

Answer 1

C-Y=3/4X

Explanation:

Answer 2

Option C.
`y=(3/4)x`

Explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

Find the value of the constant k

For the point (-8,-6)

`k=y/x=(-6/-8)=3/4`

For the point (12,9)

`k=y/x=(9/12)=3/4`

Note A single point was required to find the constant k (because the line passes through the origin)

The equation is equal to

`y=(3/4)x`