Consider the line #y=4/3x- 4#. What is the equation of the line that is parallel to this line and passes through the point (8, 6)? What is the equation of the line that is perpendicular to this line and passes through the point (8, 6)?

1 Answer
Noah G
Jul 9, 2016

Question #1:

Parallel means equal slopes. Hence, the slope of the line parallel to #y = 4/3x - 4# is #4/3#. We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.

#y - y_1 = m(x - x_1)#

#y - 6 = 4/3(x - 8)#

#y - 6 = 4/3x - 32/3#

#y = 4/3x - 14/3#

The equation of the line parallel to #y = 4/3x - 4# that passes through #(8, 6)# is #y = 4/3x - 14/3#.

Question #2:

Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to #y = 4/3x - 4# is #y = -3/4#. We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.

#y - y_1 = m(x - x_1)#

#y - 6 = -3/4(x - 8)#

#y - 6 = -3/4x + 6#

#y = -3/4x + 12#

The equation of the line perpendicular to #y = 4/3x - 4# that passes through #(8, 6)# is #y = -3/4x + 12#.

Practice exercises:

  1. Determine the equation of the line parallel to #2x + 3y = -5# that passes through the point #(-1, -9)#.

  2. Determine the equation of the line perpendicular to #y - (-2) = -1/4(x - 5)# that has the same x intercept as #2x + y = -8#

Hopefully this helps, and good luck!

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