Find the equation of the line through (5,2)which is perpendicular to the line 4y-2x=8

Answer 1

easiest way:
given 4y-2x=8 or 2x - 4y = -8

the new equation must look like
4x + 2y = c, since the slopes must be opposite reciprocals of each other.
but the point (5,2) lies on it, so ...
20 + 4 = c = 24

new equation: 4x + 2y = 24, or
2x + y = 12 , or
y = -2x + 12

Answer 2

4y-2x=8 has slope 1/2, so our new line needs slope -2
Now we have a point and a slope, so the line is
y-2 = -2(x-5)