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:
