Answer:
[tex]y=\dfrac{3}{4}x[/tex].
Step-by-step explanation:
The direct variation is defined as
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
It is given that a direct variation function contains the points (-8,-6) and (12, 9).
Substitute x=-8 and y=-6 in the above equation.
[tex]-6=-8k[/tex]
Divide both sides by -8.
[tex]\dfrac{-6}{-8}=k[/tex]
[tex]\dfrac{3}{4}=k[/tex]
The value of constant of proportionality is [tex]\dfrac{3}{4}[/tex]. So, the required equation is
[tex]y=\dfrac{3}{4}x[/tex]
At x=12,
[tex]y=\dfrac{3}{4}(12)=9[/tex]
It means, the line passing through (12,9). Hence, the equation is correct.
Therefore, the equation of the function is [tex]y=\dfrac{3}{4}x[/tex].
