Question

Consider the point P = (3,8) and the line L, given by the equation y = 3x -4.

A. Write an equation in slope-intercept of the line passing through P and parallel to line L.

B. Write an equation in slope-intercept of the line passing through P and perpendicular to line L.

Answer 1

A parallel y = 3x-1

B perpendicular y = -1/3x+9

Explanation:

y = 3x-4 is written in slope intercept form (y=mx+b) so the slope is 3.

A. If the lines are parallel they have the same slope

m parallel is 3

Using point slope form

y-y1 = m(x-x1)

y-8 = 3(x-3)

Distribute

y-8 = 3x-9

Add 8 to each side

y-8+8 = 3x-9+8

y = 3x-1

This is slope intercept form

B If we want perpendicular lines, the slope is the negative reciprocal

m perpendicular is -(1/3) = -1/3

Using point slope form

y-y1 = m(x-x1)

y-8 = -1/3(x-3)

Distribute

y-8 = -1/3x+1

Add 8 to each side

y-8+8 = -1/3x+1+8

y = -1/3x+9

This is slope intercept form