Slope-Intercept Form
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Slope-intercept form is a way of expressing a linear equation that highlights the slope and the y-intercept. The standard format is:
y = mx + b
where:
m is the slope of the line, indicating how steep it is (the change in y for a one-unit change in x),
b is the y-intercept, the point where the line crosses the y-axis (when x = 0).
Key Features:
Slope: The value of m can be positive (line rises), negative (line falls), zero (horizontal line), or undefined (vertical line).
Y-Intercept: The value of b gives the exact location on the y-axis where the line intersects, providing a quick way to graph the line.
Graphing: Knowing both the slope and the y-intercept allows for easy graphing of the line. You can start at the y-intercept and use the slope to find another point.
Example:
For the equation y = 3x + 2:
The slope m is 3 (for every 1 unit increase in x, y increases by 3),
The y-intercept b is 2 (the line crosses the y-axis at (0, 2)).
Slope-intercept form is widely used for its simplicity in identifying key features of the line and is essential for graphing and solving linear equations.