## Linear Function

**A linear function** is represented by a straight line on a graph. It indicates a linear relationship between two variables: when one changes, the other changes at a constant rate. For example:

- The count of floors vs number of windows on a high-rise building.
- The distance travelled vs time at a constant speed.
- The number of beers consumed vs blood alcohol content.

The general form of a linear function is: $f(\mathbf{\textcolor{#8ba7b9}{x}}) = \mathbf{\textcolor{#b9b28b}{m}}\mathbf{\textcolor{#8ba7b9}{x}} + \mathbf{\textcolor{#b98b99}{b}}$ where $\mathbf{\textcolor{#b9b28b}{m}}$ is the *slope* of the line and $\mathbf{\textcolor{#b98b99}{b}}$ is the *intercept*.

The slope, $\mathbf{\textcolor{#b9b28b}{m}}$, indicates how steep the line is and in which direction it points.

The point $\mathbf{\textcolor{#b98b99}{b}}$ is the y-coordinate of the point where the line intercepts on the y-axis, which tells us the value of the function when $\mathbf{\textcolor{#8ba7b9}{x}}$ is zero.