give the standard form for the equations of a line through (1,2) and perpendicular to y - 2x = 3

Question

i dont have any of the equations of a line problems so i cannot find outthe answers

Answer 1

Given point say (x1,y1) = (1,2)

line equation is y-2x = 3

Add 2x to each side.

y-2x+2x = 3+2x

y = 3+2x

Slope of the given line say m1 = 2.

We know that perpendicular line slopes product m1*m2 = -1.

Required line slope say m2.

So m2  = -1/2

Perpendicular line equation is y-2 = -1/2(x-1)

Cross multiplying.

2(y-2) =-x+1

2y-4 = -x+1

2y = -x+1+4

y = (-x+5)/2

Required line equation is y = -x/2+5/2