What is equation for the slope of a line?

Answer 1

The equation for the slope of a line in the xy plane is change in y per unit change in x.

So, if A = (xa, ya) and B = (xb, yb) are two points on the line

then slope = (yb - ya)/(xb - xa). The slope is undefined if xb = xa. In the latter case, the line is vertical, and its slope is undefined (or infinite).

If the line is a curve then you need to take the limit of the above ratio as (xb-xa) tends to zero.