Increasing linear function

Definition

An increasing linear function is a function of the form $f(x) = mx + b$ where $m > 0$. This means that as $x$ increases, $f(x)$ also increases.

5 Must Know Facts For Your Next Test

1. The slope $m$ in an increasing linear function is always positive.
2. Graphically, an increasing linear function slopes upwards from left to right.
3. $f(x) = mx + b$ represents a straight line when plotted on a Cartesian plane.
4. The y-intercept $b$ can be any real number and represents the point where the line crosses the y-axis.
5. For any two points $(x_1, f(x_1))$ and $(x_2, f(x_2))$ with $x_1 < x_2$, it holds that $f(x_1) < f(x_2)$.

Review Questions

Related terms

Slope:

The rate at which a line inclines or declines. In an equation of the form $y = mx + b$, it is represented by $m$.

Y-Intercept: The value of $y$ where the line crosses the y-axis. In an equation of the form $y = mx + b$, it is represented by $b$.

Linear Equation:

An equation that forms a straight line when graphed. It can usually be written in the form $y = mx + b$.