[tex]y = \frac{3}{4} x[/tex], x and y show direct variation.
Step-by-step explanation:
Step 1:
For x and y to show direct variation, they should be proportional to each other.
This means for x and y to be in direct variation, they should be of the form [tex]y=kx,[/tex] where k is the constant of proportionality.
If we simplify the given equation and get an equation similar to [tex]y=kx[/tex], x and y show direct variation.
Step 2:
Now we simplify the given equation,
[tex]y + \frac{3}{2} = \frac{3}{4} (x+2),[/tex]
[tex]y + \frac{3}{2} = \frac{3}{4} x + \frac{3}{4} (2) = \frac{3}{4} x+ \frac{3}{2} .[/tex]
[tex]y + \frac{3}{2} = \frac{3}{4} x+\frac{3}{2} .[/tex]
If we subtract [tex]\frac{3}{2}[/tex] from both sides, we get
[tex]y = \frac{3}{4}x.[/tex]
This is of the form [tex]y=kx[/tex] where [tex]k = \frac{3}{4} .[/tex] So x and y show direct variation.
