To obtain the equation of the line that passes through these points, you can first obtain the slope of the line, using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
And then use the point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]
So, in this case, you have
[tex]\begin{gathered} (x_1,y_1)=(5,-2) \\ (x_2,y_2)=(5,18) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{18-(-2)}{5-5} \\ m=\frac{18+2}{0} \\ m=\frac{20}{0} \end{gathered}[/tex]
Since the division by 0 is an indeterminacy then the slope of this line is not defined and these points pass through a vertical line that passes through x = 5, as you can see in the graph
Therefore, the slope of the line is undefined and the equation of the line that passes through these pair of points is
[tex]x=5[/tex]
