Answer
a) 3x +4y +8 = 0
b) 4x -3y -31 = 0
Work Step by Step
Writing equation in slope intercept form:
3x + 4y = 7
y = -$\frac{3}{4}$x + $\frac{7}{4}$
So, slope of the line is -$\frac{3}{4}$
a) line parallel to 3x + 4y = 7 and passing through point (4, -5)
(y + 5)/(x - 4) = -$\frac{3}{4}$
3x + 4y = -8
3x +4y +8 = 0
b) line perpendicular to 3x + 4y = 7 and passing through point (4, -5) will have slope $\frac{4}{3}$
(y + 5)/(x - 4) = $\frac{4}{3}$
4x - 3y = 31
4x -3y -31 = 0
