Write an equation of a line that passes through (3,-2) and is perpendicular to y=5x+4

Question

Please include an explanation as to how you solved this problem.

Answer 1

when lines are perpendicular the product of the slopes is -1

  m1*m2 = -1 where m1 and m2 are the slopes 

 

y = 5x + 4 

the slope is 5

the slope of the perpendicular line = -1/5

 

the line passes through the point (3, -2) and it passes through (x, y) any point on that line, and the slope is -1/5

using the point-slope formula or the slope -intercept formula we can write the general equation

 

point-slope                                            slope- intercept   -2 = -1/5(3) + b so b = -2 + 3/5  =( -10 + 3)/5

(y - -2) = -1/5(x -3)

y + 2 = -1/5(x - 3)

                                                            y = -1/5 x -7/5