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.

A graph showing a linear relationship between BAC and beers consumed

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

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

The point b\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 x\mathbf{\textcolor{#8ba7b9}{x}} is zero.