Linear function

Definition

A linear function is a mathematical function that creates a straight line when graphed. It can be expressed in the form $f(x) = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

5 Must Know Facts For Your Next Test

1. The slope ($m$) of a linear function indicates its steepness and direction (positive slope means upward, negative means downward).
2. The y-intercept ($b$) is the point where the line crosses the y-axis.
3. Linear functions have a constant rate of change, meaning they produce equal differences in output for equal differences in input.
4. The graph of a linear function is always a straight line.
5. $f(x) = mx + b$ can also be written as $y = mx + b$, which is known as slope-intercept form.

Review Questions

• What does the slope ($m$) of a linear function represent?
• How do you find the y-intercept from the equation of a linear function?
• Explain why the graph of a linear function is always a straight line.

Related terms

Slope-Intercept Form:

A way to express linear functions as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Slope:

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

Y-Intercept: The point at which a line crosses the y-axis, represented by $b$ in the equation $y = mx + b$.