[tex] \text{Consider the nonvertical line passing through the points }(x_1,y_1)\\ \text{and }(x_2, y_2).\\ \\ \text{we know that slope of any line is the angle between the line from the}\\ \text{positive x-axis.}\\ \\ \text{The slope of a line is given by the ratio of rise over run.}\\ \\ \text{that is the ratio of the differnce of y-coordinates to the difference}\\ \text{to the difference of the x-coordinate.} [/tex]
[tex] \text{hence the slope of the nonvertical line through the given points is}\\ \\ m=\frac{y_2-y_1}{x_2-x_1} [/tex]
