Linear function

Definition

A linear function is a mathematical function that creates a straight line when graphed. It can be represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

5 Must Know Facts For Your Next Test

1. A linear function has a constant rate of change, represented by its slope ($m$).
2. The graph of a linear function is always a straight line.
3. The y-intercept ($b$) is the point where the line crosses the y-axis.
4. The slope-intercept form of a linear equation is $y = mx + b$.
5. A horizontal line has a slope of 0, while a vertical line has an undefined slope.

Review Questions

• What does the slope ($m$) in the equation $y = mx + b$ represent?
• How do you find the y-intercept of a linear function?
• What kind of graph does a linear function produce?

Related terms

Slope: The measure of how steep a line is, calculated as rise over run ($\frac{\Delta y}{\Delta x}$).

Y-Intercept: The point where a line crosses the y-axis in Cartesian coordinates.

Slope-Intercept Form: A way to express linear equations using $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.