Find an equation of the line​ L, where L is perpendicular to y= 3/4x and passes through the point ​(4​,3​).

Question

Find an equation of the line L, where L is perpendicular to y=
3/4 and passes through the point (4,3).

Answer 1

The slope of the line with equation y = (3/4)x is 3/4.

 

The slope of any line perpendicular to the given line is -1/(3/4) = -4/3.

 

Using the point-slope form of a line, an equation of the line perpendicular to the given line which passes through the point (4,3) is:

 

             y-3 = (-4/3)(x-4)

 

             y - 3 = (-4/3)x + 16/3

 

                  y = (-4/3)x + 25/3