Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)?
a )y = –x – 2
b) 2x + 5y = −10
c) 2x − 5y = −10
d) y + 4 = –(x – 5)
e) y – 4 = (x + 5)

Answer B

Your original equation rearranged:

y = 5/2x + 3

Hence in point intercept form (y= mx + b) m is your gradient (5/2)

To be perpendicular m1 x m2 = -1

Therefore the perpendicular gradient will be the negative reciprocal (-5/2)
Sub into the point gradient formula:
y- (-4) = -5/2 (x-5)
once expanded and rearranged will become B: 2x + 5y = -10