Can lines be defined with its slope and a point on it definitely?

Question

If I get the slope of a line, and one point that is on it, then, are they define exactly ONE line?

The point–slope form of linear equations ($y - y_1 = m( x - x_1 )$) need only the slope and the coordinates of that given point. And this equation describes exactly one line.

But I'm not sure that is it enough?

Answer 1

Yes, that is enough. You can determine unambiguously whether a point is on the line from the equation. There is a problem with vertical lines in this form, however. You just need to use $x=x_1$ for that.