The equation of a line is given together with a point that i

The equation of a line is given, together with a point that is not on the line. Find the slope-intercept form of the equation of the line that passes through the given point and is (a) parallel to the given line and (b) perpendicular to the given line.

1. y = -2x + 3; (-1,2)

Solution

Given line : y = -2x +3 Point ( -1,2)

slope =-2

(a) parallel to the given line

Parallel line have same slope

So slope of this line =-2

y = mx+c . Use ( -1,2) to find c:

2 = -1*2 +c ----> c = 4

y = -2x +4

(b) perpendicular to the given line.

Slope of line shall be = -1/m = 1/2

So, y = x/2 +c Now find c using ( -1,2)

2 = -1/2 +c----> c= 5/2

y = -x/2 +5/2

2y = -x +5