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Exercises Graphs and straight lines

Example 20 from Algebra and Trigonometry, 4.1 Linear Functions

Finding the Equation of a Perpendicular Line

Find the equation of a line perpendicular to $f (x) = 3 x + 3$ that passes through the point $(3, 0) .$

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
The original line has slope $m = 3,$ so the slope of the perpendicular line will be its negative reciprocal, or $- \frac{1}{3} .$ Using this slope and the given point, we can find the equation of the line.

$\begin{matrix} g (x) & = & - \frac{1}{3} x + b \\ 0 & = & - \frac{1}{3} (3) + b \\ 1 & = & b \\ b & = & 1 \end{matrix}$
The line perpendicular to $f (x)$ that passes through $(3, 0)$ is $g (x) = - \frac{1}{3} x + 1.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given the function $h (x) = 2 x - 4,$ write an equation for the line passing through $(0, 0)$ that is

ⓐparallel to $h (x)$
ⓑperpendicular to $h (x)$

How did it go?

PreviousFinding a Line Parallel to a Given Line Next Finding the Equation of a Line Perpendicular to a Given Line Passing through a Point

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 4.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.