Perpendicular lines 2 questions

Question

through (-1,5) and parallel to the line x - 3y -7 = 0

Find the equation of the line 2x-3y-1 = 0 and through the midpoint of (1,3) and (-1,9)

Answer 1

Parallel lines have the same slope.

 

First, find the slope of the line with equation x-3y-7 = 0:

 

           -3y = -x+7

   

              y = (1/3)x - 7/3   Slope = 1/3

 

Line through (-1,5) with slope 1/3 has equation:  y - 5 = (1/3)(x - (-1))

 

                                                                       y - 5 = (1/3)x + 1/3

 

                                                                            y = (1/3)x + 16/3

 

Note:  If the line is supposed to be perpendicular to the given line, then the slope would be -1 / (1/3) = -3 instead of 1/3.