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Slope of a Line

The slope is the constant rate of change of a linear function. It can be though of as the ratio of the vertical change to the horizontal change between two points on the graph of a line.  If the two points are (x1, y1) and (x2, y2), then the vertical change is y2 - y1 and the horizontal change is x2 - x1.  Hence we can use the formula

                                   

to determine the slope of a line if we know two points on that line.  See Figure 1 below.

                                                Figure 1

Explore the following interactive example to see how the slope of a line is computed when two points are known. What observations can you make?

In general, when the slope of a linear function is positive, the function will be increasing. That is, the graph will be a line that rises from left to right. When the slope is negative, the function will be decreasing and the graph will be a line that falls from left to right. If the slope of a linear function is 0, then the function is neither increasing nor decreasing, but is constant. The graph of a constant function is a horizontal line.

Use the next interactive example to see how different values of the slope, m, affect the graph of the linear function y = mx + b.