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

Answer:

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;

$k = -\frac{8}{6} = -\frac{4}{3}$

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

$y = -\frac{4}{3}x$

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

$y = -\frac{4}{3} \cdot -2 = \frac{8}{3}$

Therefore, the direct variation related x and y is, $y = -\frac{4}{3}x$

and the value of $y =\frac{8}{3}$ when x = -2