#### Answer

$y=x-4$
$y=-\displaystyle \frac{1}{3}x+4$

#### Work Step by Step

A graphical solution to a system of linear equations is a point of intersection of two lines.
From the graph, we have two lines passing through the point (6,2),
with equations
$ x-y=4\qquad$and$\quad x+3y=12$
Slope-intercept form: solve each equation for $y$:
$\left[\begin{array}{lll}
x-y=4 & & x+3y=12\\
-y=-x+4 & & 3y=-x+12\\
y=x-4 & & y=-\frac{1}{3}x+4
\end{array}\right]$
The system:
$y=x-4$
$y=-\displaystyle \frac{1}{3}x+4$