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Exercises Graphs and straight lines

Example 21 from Algebra and Trigonometry, 4.1 Linear Functions

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

A line passes through the points $(−2, 6)$ and $\begin{matrix} m_{2} & = & \frac{- 1}{- \frac{1}{6}} \\ = & −1 (- \frac{6}{1}) \\ = & 6 \end{matrix}$ Find the equation of a perpendicular line that passes through the point $(4, 5) .$

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
From the two points of the given line, we can calculate the slope of that line.

$\begin{matrix} m_{1} & = & \frac{5 - 6}{4 - (−2)} \\ = & \frac{- 1}{6} \\ = & - \frac{1}{6} \end{matrix}$
Find the negative reciprocal of the slope.

$\begin{matrix} m_{2} & = & \frac{- 1}{- \frac{1}{6}} \\ = & −1 (- \frac{6}{1}) \\ = & 6 \end{matrix}$
We can then solve for the y-intercept of the line passing through the point $(4, 5) .$
$\begin{matrix} g (x) & = & 6 x + b \\ 5 & = & 6 (4) + b \\ 5 & = & 24 + b \\ −19 & = & b \\ b & = & −19 \end{matrix}$
The equation for the line that is perpendicular to the line passing through the two given points and also passes through point $(4, 5)$ is
$y = 6 x - 19$

Your turn

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

A line passes through the points, $(−2, −15)$ and $(2, −3) .$ Find the equation of a perpendicular line that passes through the point, $(6, 4) .$

How did it go?

PreviousFinding the Equation of a Perpendicular Line Next Using a Linear Model to Investigate a Town’s Population

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.