Answer
The lines are parallel to each other.
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$= slope and $(0, b)$ is the line's y-intercept.
(2) Parallel lines have the same slope.
(3) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Write each equation in slope-intercept form by solving for $y$ to obtain:
First Equation:
$4y+2=3x
\\4y+2-2=3x-2
\\4y=3x-2
\\\frac{4y}{4}=\frac{3x-2}{4}
\\y=\frac{3}{4}x-\frac{1}{2}$
The slope of this line is $\frac{3}{4}$.
Second Equation:
$-3x+4y=-12
\\-3x+4y+3x=-12+3x
\\4y=-12+3x
\\4y=3x-12
\\\frac{4y}{4}=\frac{3x-12}{4}
\\y=\frac{3}{4}x-3$
The slope of this line is $\frac{3}{4}$.
The two lines have the same slope, so they are parallel.