Question

When a line has an undefined slope, what will any two points on the line have in common?

Answer 1

If we take the word "undefined" mathematically, it means that it cannot be calculated. For slopes of a line, the slope is "infinte", meaning that it is a vertical line. All points on a vertical line have a common value of x.
That should answer the given question.

However, if "undefined" is taken to mean unknown, then it does not have to be a vertical line. In that case, any two points on the line will have a common slope, i.e.
\[\frac{y_2-y_1}{x_2-x_1}= constant\]