Answer
The two lines are perpendicular to each other.
Work Step by Step
RECALL:
(1) Parallel lines have equal slopes.
(2) Perpendicular lines have slopes whose product is $-1$.
(3) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope.
Write both equations in slope-intercept form to obtain:
$\bf\text{Equation 1}:$
$-3x+4y=4
\\4y=3x+4
\\\dfrac{4y}{4} = \dfrac{3x+4}{4}
\\y = \dfrac{3}{4}x + 1$
$\bf\text{Equation 2}:$
$4x+3y=5
\\3y=-4x+5
\\\dfrac{3y}{3} = \dfrac{-4x+5}{3}
\\y=-\dfrac{4}{3}x+\dfrac{5}{3}$
The two lines have slopes that are negative reciprocals of each other (product is -1).
Thus, the two lines are perpendicular to each other.
