Example

A line passes through the point $(2,-5)$ and is perpendicular to the line described by $y=2x-4$. Find an equation for the line.

Solution

The given line is in slope-intercept form. We can read its slope directly from the equation. It has slope $m=2$. The line we are working on is perpendicular to the given line. Its slope is the opposite reciprocal of $2$: $m_{\perp}=-1/2$.

Our new line has slope $-1/2$ and passes through $(2,-5)$. Its point-slope form is

or, in slope-intercept form,