Given two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], the equation of the line passing through them is
[tex]\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}[/tex]
This formula, however, only works if the points don't share any of the two coordinates. Otherwise, one of the two conditions is true:
[tex]x_1=x_2,\quad y_1=y_2[/tex]
And at least one of the denominators in the formula above will vanish.
So, if two points share the same x coordinate, they lie on the vertical line x=k, where k is the shared x coordinate.
Similarly, if two points share the same y coordinate, they lie on the horizontal line y=k, where k is the shared y coordinate.
In your case, the x coordinate is the same, so the points lie on the vertical line x=10.
