A line represented by y = 2x - 3 and a line perpendicular to it intersect at R(2, 1). What is the equation of the perpendicular line?

Question

 A line represented by y = 2x − 3 and a line perpendicular to it intersect at R(2, 1). What is the equation of the perpendicular line? 

Answer 1

The slopes of perpendicular lines are negative reciprocals.  So the slope of the line perpendicular to y = 2x-3 is -1/2.

 

An equation of the perpendicular line is y = (-1/2)x+b.  

 

  Since the point (2,1) is on the line, 1 = (-1/2)(2)+b

 

                                                    b = 2

 

An equation of the perpendicular line is y = (-1/2)x + 2.