Question

Consider the line y=-5x+7. Find the equation of the line that is perpendicular to this line and passes through the point (-3, 4). Find the equation of the line that is parallel to this line and passes through the point (-3, 4). ​

Answer 1

Perpendicular: y = 1/5x + 23/5

Parallel: y = -5x - 11

Explanation:

Perpendicular:

Take note: Perpendicular lines have the negative, reciprocal slopes:

`y-y_1=-1/m(x-x_1)\\y-4=1/5(x+3)\\y-4=1/5x+3/5\\y=1/5x+3/5+20/5\\y=1/5x+23/5`

Parallel:

Take note: Parallel lines have the same slope:

`y-y_1=m(x-x_1)\\y-4=-5(x+3)\\y-4=-5x-15\\y=5x-15+4\\y=5x-11`