Question

In the following exercises, find the equation of a line containing the given points. Write the equation in slope-intercept form.

$(-2,1)\mathrm{and}(-2,-4)$

Short answer

Equation of line is:$\mathrm{x}=-2$

No slope-intercept form.

Step-by-step solution

Step 1. Given Data

Points:$(-2,1)\mathrm{and}(-2,-4)$

Step 2. Finding the slope using given points

The slope of the line through $(-2,1)\mathrm{and}(-2,-4)$:

$$\begin{gathered} \mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\left(1\right) \\ \mathrm{where}, \\ {\mathrm{y}}_2=-4 \\ {\mathrm{y}}_1=1 \\ {\mathrm{x}}_2=-2 \\ {\mathrm{x}}_1=-2 \\ \mathrm{Putting}\mathrm{values}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{m}=\frac{-4-1}{-2-(-2)}=\frac{-5}{-2+2}=\frac{-5}{0} \\ \mathrm{The}\mathrm{slope}\mathrm{is}\mathrm{undefined}. \end{gathered}$$

Step 3. Equation of the line. 

Since the Slope is undefined which means it is a vertical line.

Both of the points have an x-coordinate of $-2$.

So, our equation of a line is:$\mathrm{x}=-2$