Slope measures the steepness of a line. The graph of a line with positive slope goes upward from left to right and the graph of a line with negative slope goes downward from left to right. The slope of the line <EQUATION>. Solve the following problems. Click “Submit” when finished.

You can find the slope of a line by finding the <EQUATION> and <EQUATION> of different points on the line. Now, let’s see how to find the slope of a line if you don’t know its equation.

The building in the picture is on a hill. Can we find the slope of the hill? Slope is the rise divided by the run. So, we need to measure the rise and run. We can do this using a ruler. The rise is <EQUATION> inches and the run is <EQUATION> inches. Using a calculator to do the division, the slope is approximately <EQUATION>. So we found the slope of the hill to be <EQUATION> without knowing any points on the line.

Let’s find the slope of this line. We can pick two points on the line, and measure the rise and the run between the points. There are many points on this line. Does it matter which pair of points we pick? Let’s see what happens with different pairs.

First, let’s find the slope using the first two points. To get from the point on the left to the point on the right we must go up <EQUATION> units. So the rise is <EQUATION>. To get from the point on the left to the point on the right we have to go right <EQUATION> units. So the run is <EQUATION>. The slope is rise over run, or <EQUATION>. Now let’s find the slope using a different pair of points.

To get from the point on the left to the point on the right we have to go up <EQUATION> units and right <EQUATION> units. So the rise is <EQUATION> and the run is <EQUATION>. Therefore, the slope is <EQUATION>, which can be simplified to <EQUATION>. As you have seen, the slope of the line is the same, no matter which pair of points we pick to find the rise and the run.

Let’s find the slope of another line. We can pick two points on the line, and measure the rise and the run between the points. You know that the slope of the line is the same no matter which two points we choose. There are many points on this line, but it will be easier to find the rise and run between two points that lie at intersections of the gridlines. So, let’s use the two red points to calculate the slope of the line.

To get from the point on the left to the point on the right we must go up <EQUATION> units. So the rise is <EQUATION>. To get from the point on the left to the point on the right we must go right <EQUATION> units. So the slope is <EQUATION> divided by <EQUATION>, which is approximately <EQUATION>.

Find the slope of the line. Click “Submit” when finished.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education