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.

A parallel y = 3x-1

B perpendicular y = -1/3x+9

Step-by-step 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

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