Answer:
Given equation:
[tex]1+\frac{1}{2}(y-2)=\frac{3}{2}x[/tex]
Solving for [tex]y[/tex]
In order to solve for [tex]y[/tex] we will isolate [tex]y[/tex] on one side.
Using distribution.
[tex]1+\frac{1}{2}y-(\frac{1}{2}\times2)=\frac{3}{2}x[/tex]
[tex]1+\frac{1}{2}y-1=\frac{3}{2}x[/tex]
Simplifying.
[tex]\frac{1}{2}y=\frac{3}{2}x[/tex]
Multiplying both sides by 2 to isolate [tex]y[/tex] on left side.
[tex]2\times \frac{1}{2}y=2\times \frac{3}{2}x[/tex]
∴ [tex]y=3x[/tex]
So, we get a proportional equation in the form of
[tex]y=kx[/tex]
where [tex]k[/tex] represents the constant of proportionality.
Thus the equation [tex]y=3x[/tex] shows that [tex]y[/tex] directly varies with [tex]x[/tex]
