Write the equation of the line perpendicular to y=-2x+5 and passes through the point (-4;5)?

Question

this is part of my final...please help
HOW CAN YOU TELL THAT THE TWO LINES ARE PERPENDICULAR JUST BY THE SLOPES?

Answer 1

Given line is y =-2x+5

Slope of the line say m1 = -2

perpendicular line slope say m2 .

m1*m2 = -1

-2m2 = -1

Divide by negitive 2 to each side.

m2 = -1/-2

m2 = 1/2

Line equation through (-4,5) and m2 = 1/2

y-y1 = m(x-x1)

y-5 = 1/2(x+4)

y-5 = (1/2)x+2

Add 5 to each side.

y-5+5 = (1/2)x+2+5

y = (1/2)x+7

Perpendicular line equation is y = (1/2)x+7.