Another writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line y=7x-7

Find the equation of the line that is perpendicular to this line and passes through the point (−3,  6)

Find the equation of the line that is parallel to this line and passes through the point (−3,  6)

Answer 1

Perpendicular lines have opposite, reciprocal slopes, like 3 and -1/3 or 4/3 and -3/4. Plug in the point given and solve for b.

y = mx + b

6 = (-1/7)(-3) + b

6 = (3/7) + b

42/7 = (3/7) + b

b = 39/7

y = (-1/7)x + 39/7

Parallel lines have the saaaaame slope, right? Do the same and I bet you'll get it!

Answer 2

y=7x -7

parallel line through the point (-3,6)

is: y-6 = 7(x+3)

or y = 7x +27

perpendicular line through (-3,6)

is: y-6 = (-1/7)(x+3)

or y = -x/7 -3/7 + 42/7

or y =-x/7 +39/7

parallel lines have the same slope

if the linear equation is solved for y, then the slope = the coefficient of the x term= 7

perpendicular lines have negative inverse slopes = the negative inverse of the coefficient of the x term= -1/7