The Slope of a Line
Definition  The Slope of a LineThe slope of a line is a measure of how quickly or slowly the line is rising. Another way to think of it would be that the slope measures the steepness of a line. A slope that's very small, i.e. close to zero, indicates a line that's rising very slowly where a large slope indicates that the line is very steep. If I give you two points, $(x_1, y_1)$ and $(x_2, y_2)$ then you can calculate the slope of the line connecting them using the slope formula: $$ m = \frac{y_1  y_2}{x_1  x_2}$$The applet on the right gives you a chance to see what various slopes look like. Enter a numeric value into the text book, click on the "Draw Line" button and the tool will draw a line with the slope you specified. 

Example 1Find the slope of the line through the points (3, 10) and (4, 5). This is a straightforward application of the formula. I'm going to let the numbers in the (3, 10) point by the x_{1} and y_{1} values and the numbers in the (4, 5) point will be the x_{2} and y_{2}. Substituting those numbers into the formula gives us: $$m=\frac{y_1y_2}{x_1x_2}=\frac{105}{34}=\frac{5}{1}=5$$

Example 2Find the slope of the line through the points (2, 8) and (4, 6). This is also straightforward application of the formula but watch carefully how I deal with the negative signs. $$m=\frac{y_1y_2}{x_1x_2}=\frac{8(6)}{24}=\frac{8 + 6}{6}=\frac{14}{6}=\frac{8}{3}$$
