The slope-intercept form of the equation of a nonvertical line with slope m and y-intercept b is y = mx + b or can be expressed in function notation by replacing y with f(x), f(x) = mx + b. Functions in this form are linear functions. If a linear function is in slope-intercept form, we can use the y-intercept and the slope to obtain its graph.

Graphing y = mx + b using the slope and y-intercept:

1. Plot the point containing the y-intercept on the y-axis. Yhis is the point (0, b).

2. Obtain a second point using the slope m. Write m as a fraction (if it is not a fraction), and use rise and run, starting at the point containing the y-intercept, to plot this point.

3. Use a straightedge to draw a line through the two points (the line continues indifinetly in both directions).

Example: Graph the linear functiony f(x) = -2x + 1

Solution:

Step 1. Find the slope m and the y-intercept.

m = -2 and y-intercept is 1

Step 2. Plot the point containing the y-intercept on the y-axis.

Plot (0, 1)

Step 3. Obtain a second point using the slope m. Write m as a fraction (if it is not a fraction), and use rise and run, starting at the point containing the y-intercept, to plot this point.

m = -2/1 = Rise/Run

Plot the second point by starting at (0, 1). Move 2 units down (the rise) and 1 unit to the right (the run). so we obtain a second point on the line, (1, -1).

Step 4. Use a straightedge to draw a linethrough the two points.

Now you have the graph of the linear function f(x) = -2x + 1.