The slope will be the same for a straight line no matter which two points you pick as you know. In geometry you can use the slope to plot points on a line including lines that define the shape of a polygon. Drag A and B to some new.
To find the slope you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
The slope formula is the vertical change in y divided by the horizontal change in x sometimes called rise over run. Using two points on the line calculate the rise and the run and express it as a fraction rise over run. Slope is equal to change in y this is the Greek letter delta look likes a triangle but its shorthand for change in y over change in x. In the above diagram Drag the points A and B around and notice how the calculated slope changes.