Given,
The line is passing through the points (5,2), (5,6).
The standard equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substituting the values of coordinates then,
[tex]\begin{gathered} y-2_{}=\frac{6_{}-2_{}}{5_{}-5_{}}(x-5) \\ y-2=\frac{4_{}}{0_{}} \\ y-2=\infty\mleft(x-5\mright) \\ \frac{y-2}{\infty}=x-5 \\ 0=x-5 \\ x=5 \end{gathered}[/tex]Hence, the equation of line passing through point (5,2) and (5,6) is x=5.
