Question

A line that passes through the points (2,1) and (k,5) is perpendicular to the line y=3x-9. Find the value of k

Answer 1

Since we know it is perpendicular to $y=3x-9$, we know the slope of the line is the opposite reciprocal of 3, or $-\frac{1}{3}$. Then we can use the two points in the slope formula to solve for k:
$-\frac{1}{3}=\frac{5-1}{k-2}$
$-\frac{k-2}{3}=4$
$k-2=-12$
$k=-10$