Linear function

Definition

A linear function is a polynomial function of degree one, which can be written in the form $f(x) = mx + b$ where $m$ and $b$ are constants. The graph of a linear function is a straight line.

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 y-intercept of a linear function is the value of $f(x)$ when $x=0$, denoted as $b$.
3. The domain and range of a linear function are both all real numbers, unless otherwise restricted.
4. The slope-intercept form $y = mx + b$ makes it easy to identify the slope and y-intercept directly from the equation.
5. Parallel lines have equal slopes, while perpendicular lines have slopes that are negative reciprocals.

Review Questions

• What is the general form of a linear function?
• How do you determine the slope and y-intercept from the equation $y = 3x - 4$?
• What characteristic of linear functions ensures their graphs will always be straight lines?

Related terms

Slope: The measure of steepness or inclination of a line, calculated as the ratio of vertical change to horizontal change between two points on the line.

Y-Intercept: The point where a line crosses the y-axis, represented as $(0, b)$ in the equation $y = mx + b$.

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