Question

Write the equation of the line that passes through (2,5) and (2,-13).

Answer 1

To find the equation of the line that passes through these points you can first find the slope of the line using this formula:

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}$

In this case, you have

$\begin{gathered} (x_1,y_1)=(2,5) \\ (x_2,y_2)=(2,-13) \end{gathered}$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-13-5}{2-2} \\ m=\frac{-18}{0} \end{gathered}$

Since it is not possible to divide by zero then the slope of this line is not defined. Then the line through the given points is a vertical line.

By definition, the slope of a vertical line is not defined, and its representation is indicated by the coordinate where it crosses the x-axis.

Therefore, the equation of the line that passes through the given points is:

$x=2\text{ }$

As you can see in the following graph