At the end of this lesson, students will be able to:
- Identify the slope and y−intercept of equations and graphs.
- Graph an equation in slope-intercept form.
- Understand what happens when you change the slope or intercept of a line.
- Identify parallel lines from their equations.
Terms introduced in this lesson:
Teaching Strategies and Tips
Use Examples 1 and 2 to make observations such as:
m<0 when a line slants downward and m>0 when it slants upward.
m=0 when a line is horizontal.
b<0 when the y−intercept is below the x−axis and b>0 when it’s above the x−axis.
b=0 when a line passes through the origin.
Use the slope-intercept method to graph lines as an alternative to plotting and joining two intercepts.
With a graphing utility, demonstrate the effects on a line when changing m and b one at a time in an equation in slope-intercept form. Make observations such as:
- The larger the m, the steeper the line.
- Negative slopes can also represent steep lines. The smaller the m (more negative), the steeper the line.
- Slopes approximately equal to zero represent lines that are almost horizontal.
- Changing the intercept shifts a line up/down.
- Parallel lines have the same slope but different y−intercepts.
In Example 2, use the marked lattice points and/or intercepts in the slope calculation for each line. Using these points allows students to obtain exact answers. See also Review Questions, Problems 2 and 3.