Once students have mastered the concept of slope = rise/run, the following investigation can be used to help them discover that in the equation y = mx + b, m equals the slope. Each equation can be graphed using a graphing utility. Students can then choose two points on the line and find the slope using m = rise/run as the definition of slope. The following can be printed and used as a worksheet.

Investigation

Use a graphing utility to graph the following equations and make a sketch of the graph. Then choose two points on the line and find the slope of the line.

1. y = x

2. y = 2x

3. y = 4x

4. y = 6x

9. y = -x

10. y = -3x

11. y = -4x

12. y = -5x

16. What conclusions can you draw? What relationships do you notice?

17. Predict what the graph of y = -7x will look like by making a sketch. Then use a graphing utility to look at the actual graph. If your prediction is incorrect, go back and look again at the given equations and their slopes and see if you notice anything that you missed the first time.