Answer
The lines are perpendicular.
Work Step by Step
RECALL:
(i) Two lines are parallel if they have (a) equal slopes or (b) undefined slopes.
(ii) Two lines are perpendicular if they have (a) slopes whose product is −1 or (b) if one has a zero slope and the other has an undefined slope.
(iii) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b=y-intercept.
Write both equations in slope-intercept form to have:
Equation 1:
$-3x+4y=4
\\4y=3x+4
\\y=\dfrac{3x+4}{4}
\\y=\dfrac{3}{4}x+1$
Equation 2:
$4x+3y=5
\\3y=-4x+5
\\y=\dfrac{-4x+5}{3}
\\y=-\dfrac{4}{3}x+\dfrac{5}{3}$
Product of slopes:
$\frac{3}{4}\times-\frac{4}{3}=1$
The lines have slopes whose product is equal to −1.
Thus, the lines are perpendicular.
