Example

An engineer working with a certain voltage-controlled amplifier finds that an input of 1.32 volts is amplified to 14.00 volts, while an input of 3.79 volts has an output of 8.00 volts. Assuming the gain is linear, find an equation relating the input and output voltages.

Solution

Let's work with ordered pairs of the form (input,output). We are looking for an equation of the line that passes through the points $(1.32,14.00)$ and $(3.79,8.00)$.

Let's start by computing slope:

Now using this slope and the point $(1.32,14.00)$, we obtain the point-slope form

Solving for $y$ and rounding to the nearest hundredth gives

or