Finding equations of parallel and perpendicular lines

Question

Consider the line y=7/2x+6

Find the equation of the line that is perpendicular to this line and passes through the point (-7,-4)

Find the equation of the line that is parallel to this line and passes through the point (-7,-4)

 

Thank you in advance! :D

Answer 1

y=7/2x+6

 It's in the form of y=m1x+c, so the slope or m1 = 7/2

A line perpendicular to this has a slope m2= -2/7 (since m1.m2=-1, for lines perpendicular to each other)

This line passes through (-7, -4). So the equation of the line in the form y-y1 =m (x-x1)

or, y+4=-2/7(x+7)

7y+28= -2x-14

2x+7y=-42

 

A line parallel to the given line has a slope m3= 7/2 (since m1=m3, for lines parallel to each other)

This line passes through (-7, -4). So the equation of the line in the form y-y1 =m (x-x1)

or, y+4=7/2(x+7)

2y+8=7x+49

7x-2y= -41

 

Answer 2

Perpendicular:

m = -1/(7/2) = -2/7

 

In point-slope form,

y - (-4) = (-2/7)[x - (-7)]

 

y + 4 = (-2/7)(x + 7)

 

Parallel:

 

m = 7/2

 

In point-slope form,

 

y - (-4) = (7/2)[x - (-7)]

 

y + 4 = (7/2)(x + 7)

 

 

Answer 3

The slope of the original line is 7/2, so a parallel line has to have the same slope.  A perpendicular line has the negative inverse slope or -2/7.  Use the point slope form I gave you earlier to find the 2 equations.