What is an equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x-3y=18?

Question

Now this one is definitely hard for me

Answer 1

slope of line ax + by = c is -a/b, so slope of line 4x - 3y = 18 is 4/3.

slope of perpendicular line is negative reciprocal or -3/4

point intercept equation of line is y-y1 = m(x - x1) where m is slope and (x1,y1) is point line passes through, so given point line passes through is (8,-8):

y +8 = -3/4(x-8)

y+ 8 = -3/4 x + 6

4y + 32 = -3x + 24 (multiply through by 4)

3x + 4y = -8 (modify to ax + by = c format)