find the equation of the line passing through (4,1) and perpendicular to the line 3x+2y-6=0.

Question

find the equation of the line passing through (4,1) and perpendicular to the line 3x+2y-6=0.

Answer 1

If 3x+2y-6=0, then 2y=-3x+6

 

                             y = (-3/2)x + 3  This line has slope -3/2

 

The slope of any line perpendicular to the given line is -1/(-3/2) = 2/3.

 

Equation of line through (4,1) with slope 2/3:   y-1 = (2/3)(x-4)

 

                                                                  y-1 = (2/3)x - 8/3

 

                                                                    y = (2/3)x - 5/3