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Exercises Graphs and straight lines

Example 4.67 from Elementary Algebra, 4.6 Find the Equation of a Line

Find the Equation of a Line: example 4.67

Find an equation of a line perpendicular to $x = 5$ that contains the point $(3, −2)$ . Write the equation in slope–intercept form.

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
Again, since we know one point, the point–slope option seems more promising than the slope–intercept option. We need the slope to use this form, and we know the new line will be perpendicular to $x = 5$ . This line is vertical, so its perpendicular will be horizontal. This tells us the $m_{⊥} = 0$ .

Identify the point. $(3, −2)$

Identify the slope of the perpendicular line. $m_{⊥} = 0$

Substitute the values into $y - y_{1} = m (x - x_{1})$ . $\begin{matrix} y - y_{1} = m (x - x_{1}) \\ y - (−2) = 0 (x - 3) \\ y + 2 = 0 \end{matrix}$

Simplify. $y = −2$

Sketch the graph of both lines. Do they appear to be perpendicular?

Your turn

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

Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $(4, −5)$ . Write the equation in slope–intercept form.

How did it go?

PreviousFind the Equation of a Line: example 4.66 Next Find the Equation of a Line: example 4.68

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 4.6, 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.