Determine equation in Ax+By+C=0 for the line, parallel to 3x-4y+4=0 with the same x-intercept as y=1/2x-4

All lines parallel to line 3x − 4y + 4 = 0 will have the form 3x − 4y + C = 0

Line y = 1/2 x − 4 has x-intercept = (8,0)

So line parallel to line 3x − 4y + 4 = 0 passes through point (8,0)

3(x−8) − 4(y−0) = 0
3x − 4y − 24 = 0

3x-4y+4=0
4y = 3x + 4
y = (3/4)x + 1

Slope = 3/4

x intercept:
y = (1/2)x-4
0 = (1/2)x-4
4 = x/2
x = 8
so (x = 8 , y = 0)

Ax+By+C=0
(3/4)x -y + C = 0
y = (3/4)x + C
0 = (3/4)(8) + C
0 = 6 + C
C = -6
(3/4)x -y -6 = 0

(value for B, is arbitrary, I picked -1 because it's the easiest to work with, ie. turn into y =ax + b form)