Question

What is the slope of any line perpendicular to the line passing through `(-5,1)` and `(11,-4)`?

Answer 1

A line `b` perpendicular to another line `a` has a gradient of `m_b = -1/m_a` where `m_a` is the gradient (slope) of line `a`. In this case the slope is `(16)/5`.

Explanation:

To find the gradient (slope) of the given line through the points `(-5, 1)` and `(11, -4)` use the formula:

`m=(y_2-y_2)/(x_2-x_1) = (-4-1)/(11-(-5)) = -5/16`

Lines parallel to this line will have the same slope, lines perpendicular to it will have slope `-1/m`.

In this case, that means the slope of any perpendicular line will be `(16)/5`.