Slope

Many physical relationships in science and engineering may be expressed by plotting a straight line. The slope(m), or steepness, of a straight line tells us the amount one parameter changes for a certain amount of change in another parameter. For a straight line, slope is equal to rise over run, or :

Since slope m is a measure of the steepness of a line, a slope has the following characteristics:

1. A horizontal line has zero slope.

2. A line that rises to the right has positive slope.

3. A line rising to the left has negative slope.

4. A vertical line has undefined slope because the calculation of the slope would involve division by zero. (Dy/Dx approaches infinity as the slope approaches vertical.) On a graph the slope can be found by selecting two points, forming a right triangle, counting the number of units in the rise and the run, and then dividing those 2 values.

A better method is to find the coordinate of two points on the line, say (1 ,y1) and (x2 ,y2), then use the formula:

Example: What is the slope of the line passing through the points (20, 85) and (30, 125)?