Example4.9.11Building a Table of \(x\)- and \(y\)-values

To make a table, we could substitute \(x\) for various numbers and use algebra to find the corresponding \(y\)-values. Let's start with \(x=-2\text{,}\) planning to move on to \(x=-1,0,1,2\text{.}\)

\begin{align*} 3x+4y\amp=12\\ 3(\substitute{-2})+4y\amp=12\\ -6+4y\amp=12\\ 4y\amp=12\addright{6}\\ 4y\amp=18\\ y\amp=\divideunder{18}{4}\\ y\amp=\frac{9}{2} \end{align*}

The first point we found is \(\left(-2,\frac{9}{2}\right)\text{.}\) This has been a lot of calculation, and we ended up with a fraction we will have to plot. And we have to repeat this process a few more times to get more points for the table. The table method is generally not a preferred way to graph a line in standard formĀ (4.7.1). Let's look at other options.