Linear Functions

A linear function is a rule that takes an input and produces an output in a way that forms a straight line when plotted on a graph.

Mathematically, you write linear functions using the slope-intercept form.

You can use linear functions to model scenarios in which a quantity changes at a constant rate. One important application involves how pressure changes as you dive deeper into freshwater.

On a graph, this linear relationship forms a straight line, with the y-intercept showing a starting pressure of 100 kilopascals at 0 meters depth.

As you descend, water adds 9.81 kilopascals of pressure for every meter of depth. This constant rate of change is our slope, m.

Substituting the slope and y-intercept into slope-intercept form gives the linear equation. For recreational diving, the depth is limited to 0 to 40 meters. So, the domain is 0 to 40 meters.

To find the pressure range, we look at the pressure at the two ends. At 0 meters, the pressure is 100 kilopascals. And at 40 meters, it is 492.4 kilopascals. So, the pressure range is from 100 to 492.4 kilopascals.