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Exercises Graphs and straight lines

Example 4.64 from Elementary Algebra, 4.6 Find the Equation of a Line

Find the Equation of a Line: example 4.64

Find an equation of a line that contains the points $(−2, 4)$ and $(−2, −3)$ . 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, the first step will be to find the slope.

Find the slope of the line through $(−2, 4) and (−2, −3)$ . $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$m = \frac{−3 - 4}{−2 - (−2)}$

$m = \frac{−7}{0}$

The slope is undefined.

This tells us it is a vertical line. Both of our points have an x-coordinate of $−2$ . So our equation of the line is $x = −2$ . Since there is no $y$ , we cannot write it in slope–intercept form.
You may want to sketch a graph using the two given points. Does the graph agree with our conclusion that this is a vertical line?

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 containing the points $(5, 1)$ and $(5, −4)$ .

How did it go?

PreviousFind the Equation of a Line: example 4.63 Next Find the Equation of a Line: example 4.65

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.