A. To find the slope of a line through 2 points, (x0,y0) and (x1,y1), use the following formula:
B. Notice, it does not matter if you subtract y1 - y0 or y0 - y1 as long as you are consistent with the x-values also. In other words, if you subtract y0 - y1 you should subtract x0 - x1.
C. Examples
Ex [1] Find the slope of the line passing through the points (6,-1) and (4, 5). ________.
a. First, subtract the y-values: 5 - (-1) = 6.
b. Subtract the x-values: 4 - 6 = -2.
c. The answer is -6/2 = -3.
Ex [2] Find the slope of the lines passing through the points (1,1) and (-2,3). ________.
a. First, subtract the y-values: 1 - 3 = -2.
b. Subtract the x-values: 1 - (-2) = 3.
c. The answer is -2/3.
D. Sometimes the question might ask for the perpendicular slope of a line passing through the two points. In this case, simply find the negative reciprocal. So for Ex [1] the perpendicular slope would be 1/3 and for Ex [2] the perpendicular slope would be 3/2.