Identifying Parallel and Perpendicular Lines

Given the functions below, identify the functions whose graphs are a pair of parallel lines and a pair of perpendicular lines.

\begin{matrix} f (x) & = & 2 x + 3 & h (x) & = & - 2 x + 2 \\ g (x) & = & \frac{1}{2} x - 4 & j (x) & = & 2 x - 6 \end{matrix}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Parallel lines have the same slope. Because the functions $f (x) = 2 x + 3$ and $j (x) = 2 x - 6$ each have a slope of 2, they represent parallel lines. Perpendicular lines have negative reciprocal slopes. Because −2 and $\frac{1}{2}$ are negative reciprocals, the functions $g (x) = \frac{1}{2} x - 4$ and $h (x) = −2 x + 2$ represent perpendicular lines.

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