Slope-Intercept Form
Graphing Horizontal Lines
What happens to the slope-intercept equation when m = 0? Remember that slope is the ratio of rise over run. For a slope to be zero, then the rise must be zero. In other words the line does not rise, which means it must be horizontal. Plugging m = 0 into the slope-intercept equation produces the following equation:
Consider the equation y = 4. There is no x-term, thus m = 0 and b = 4. So the graph will be a line that crosses the y-axis at 4 and does not rise.
Using the points (-3, 4) and (5, 4), to calculate the slope of this line confirms that the slope of this line is zero.
All horizontal lines have a slope of zero. The line above contains the points (-1, 4), (0, 4), (1, 4), (2, 4), etc. Notice that the y-value is always 4. Therefore the equation of a horizontal line will have the form y = b. For example, y = -3 will graph as a horizontal line crossing the y-axis at -3.