Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5?

Answer 1

A line perpendicular to y = (-2/3)x + 5 has a slope of (+3/2).

Use the slope-intercept formula here, and find b:

y = mx + b becomes 1 = (3/2)(8) + b.  Multiplying all terms by 2, we get

2 = 24 + 2b.  Thus, 2b = -22, b = -11, and the equation of the line is y = (3/2)x - 11.