q problem (algebra)?

Question

Find the value for "q" given that qx + 2y = -5 is perpendicular to the line 2x - 4y = 3.

Answer 1

2 y = - q x - 5
y = (- q/2) - 5/2

2 x - 4 y = 3
4 y = 2 x - 3
y = (1/2) x - 3/4

(1 / 2) (- q / 2) = - 1
- q / 4 = - 1
q = 4

Answer 2

y = -q/2 - 5 and y = 1/2x - 3/4

for two lines to be perpendicular to each other the product of their slope = -1

-q/2 * 1/2 = -1
q = 4

Answer 3

2x - 4y = 3
4y = 2x - 3
y = x/2 - 3/4

2y = -qx - 5
y = -qx/2 - 5/2

-qx/2 = -2x { -2x is the perpendicular slope of x/2 }
-q/2 = -2 { Divide both sides by x }
-q = -4 { Multiply both sides by 2 }
q = 4 { Multiply (or divide) both sides by -1 }