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;
[tex]k = -\frac{8}{6} = -\frac{4}{3}[/tex]
Now, to find the value of y when x = 2 we have;
[tex]y = -\frac{4}{3}x[/tex]
Substitute the given value of x =-2 we have;
[tex]y = -\frac{4}{3} \cdot -2 = \frac{8}{3}[/tex]
Therefore, the direct variation related x and y is, [tex]y = -\frac{4}{3}x[/tex]
and the value of [tex]y =\frac{8}{3}[/tex] when x = -2
