Question

Consider the line y=-2x+3.

Find the equation of the line that is perpendicular to this line and passes through the point (5, 6).
Find the equation of the line that is parallel to this line and passes through the point (5,6).

Answer 1

See explanations below

Explanation:

Consider the line y=-2x+3.

The equation in point slope form is expressed as y-y0=m(x-x0)

m is the slope

(x0,y0) is the point

If the Line is parallel, slope m = -2

Substitute

y-6 = -2(x-5)

y-6 = -2x+10

y+2x = 10+6

y+2x = 16

Is the line is perpendicular

Slope m = -1/-2

m = 1/2

Substitute into the formula

y - 6 = -1/2(x-5)

2(y-6) = -(x-5)

2y-12 = -x+5

2y+x = 5+12

2y+x = 17