Question

Suppose y varies directly with x, and y = 8 when x = –6. What direct variation equation relates x and y? What is the value of y when x = –2?

Answer 1

B -4/3=-1.33 and 8/3=2.6666

Answer 2

Direct variation states that the relationship between two variables in which one is a constant multiple of the other one.

In other words, when one variable changes the other one changes in proportion to the first.

i.e, if y is directly proportional to x then, the equal will be of the form is, y= kx where k is the constant of variation.

Given: y varies directly with x, and y = 8 when x = –6

By definition of direct variation,

y = kx

Substitute the values of x = -6 and y=8 to solve for k;

8 = -6k

Divide both sides by -6 we get;

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

Now, to find the value of y when x = 2 we have;

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

Substitute the given value of x =-2 we have;

`y = -(4)/(3) \cdot -2 = (8)/(3)`

Therefore, the direct variation related x and y is,
`y = -(4)/(3)x`

and the value of
`y =(8)/(3)` when x = -2