Find an equation of the line that contains the given point and is perpendicular to the given line

Question

Find an equation of the line that contains the given point and is perpendicular to the given line

(2,-6), 3x-5y=2

Answer 1

3x-5y = 2 solve for y

5y= 3x-2

y = (3/5)x - 2/5 3/5 is the slope. You want the negative inverse of 3/5: -5/3 as the slope of the perpendicular line

y=-5x/3 + b where b is the y intercept. to calculate b, plug in the point x=2,y=-6

-6 = -5(2)/3 + b

b = -6 +10/3 = -8/3

y = -5x/3 - 8/3 or

5x+3y = -8 is the perpendicular line through (2,-6)

5(2)+3(-6) = 10-18 = -8