Example 4.9.12 Using intercepts

Next, we will try graphing \(3x+4y=12\) using intercepts. We set up a small table to record the two intercepts:

\(x\)-value \(y\)-value Intercept
\(x\)-intercept \(0\)
\(y\)-intercept \(0\)

We have to calculate the line's \(x\)-intercept by substituting \(y=0\) into the equation:

\begin{align*} 3x+4y\amp=12\\ 3x+4(\substitute{0})\amp=12\\ 3x\amp=12\\ x\amp=\divideunder{12}{3}\\ x\amp=4 \end{align*}

And similarly for the \(y\)-intercept:

\begin{align*} 3x+4y\amp=12\\ 3(\substitute{0})+4y\amp=12\\ 4y\amp=12\\ y\amp=\divideunder{12}{4}\\ y\amp=3 \end{align*}

So the line's \(x\)-intercept is at \((4,0)\) and its \(y\)-intercept is at \((0,3)\text{.}\) Now we can complete the table and then graph the line:

\(x\)-value \(y\)-value Intercepts
\(x\)-intercept \(4\) \(0\) \((4,0)\)
\(y\)-intercept \(0\) \(3\) \((0,3)\)
Table 4.9.13 Intercepts of \(3x+4y=12\)
Figure 4.9.14 Graph of \(3x+4y=12\)