Question

Choose the formula for finding the slope m of a nonvertical line that contains the two distinct points left parenthesis x 1 comma y 1 right parenthesisx1,y1 and left parenthesis x 2 comma y 2 right parenthesisx2,y2.

Answer 1

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

$\text{hence the slope of the nonvertical line through the given points is}\\ \\ m=\frac{y_2-y_1}{x_2-x_1}$