a line to have no equation in point-slope form or to have infinitely many, but it is not possible that there is only one.

Question

Explain why it is possible for a line to have no equation in point-slope form or to have infinitely many, but it is not possible that there is only one.

Answer 1

If slope is undefined, as is the case for any vertical line, then it is of the form x = constant and it's not possible to represent it in point-slope form.

 

All other lines can be put into the form y = mx + b, including horizontal lines (when m = 0).

 

In the statement of the question, "or to have infinitely many" is not helpful.