Question

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

y = –4/3x
y = –3/4x
y = 3/4x
y =4/3 x

Answer 1

y=3/4x, as the sign of the function does not change, and the y value is less than the x value

Answer 2

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`

With the point 1 or the point 2 find the value of the constant k

Point 1 (-8,-6)

x=-8

y=-6

substitute

`(y)/(x)=k`

`(-6)/(-8)=k`

`k=(3)/(4)`

therefore

the equation is

`y=(3)/(4)x`

the answer is the option

`y=(3)/(4)x`