What is the equation of the line that passes through the point (6,8) and is perpendicular to a line with equation y= 3/2x +5

Answer 1

The slope of a perpendicular line has

(1) opposite sign of other line

(2) inverse slope of the other line

Therefore, the slope of the perpendicular line is

m = - 2/3

Now,

Y = (-2/3) * x + b

8 = (-2/3) * 6 + b

8 = - 12/3 + b

8 + 4 = b

b = 12

Answer

Y = (-2/3) * x + 12