Notes by Lex Toumbourou

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.

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