Answer
The graphs are perpendicular lines.
Work Step by Step
RECALL:
(1) In the slope-intercept form of a line's equation $y=mx+b$, $m$=slope and $b$ is the y-coordinate of the y-intercept.
(2) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocals of each other).
Write both equations in slope-intercept form to obtain:
First Equation:
$x-2y=3
x-2y+2y-3=3+2y-3
\\x-3=2y
\\\frac{x-3}{2}=\frac{2y}{2}
\\\frac{1}{2}x-\frac{3}{2}=y
\\y=\frac{1}{2}x-\frac{3}{2}$
Second Equation:
$4x+2y=1
\\4x+2y-4x=1-4x
\\2y=1-4x
\\2y=-4x+1
\\\frac{2y}{2}=\frac{-4x+1}{2}
\\y=-2x +\frac{1}{2}$
Note that two equations have the slopes $\frac{1}{2}$ and $-2$.
Since $\frac{1}{2} \cdot (-2) = -1$, then the graphs of the two equations are perpendicular lines.