###### Example4.9.12Using 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 $$0$$ $$3$$ $$(0,3)$$
in-context