###### Example 4.9.15 With Slope Triangles

We can always rearrange \(3x+4y=12\) into slope-intercept form (4.5.1), and then graph it with the slope triangle method:

\begin{align*}
3x+4y\amp=12\\
4y\amp=12\subtractright{3x}\\
4y\amp=-3x+12\\
y\amp=\divideunder{-3x+12}{4}\\
y\amp=-\frac{3}{4}x+3
\end{align*}

With the \(y\)-intercept at \((0,3)\) and slope \(-\frac{3}{4}\text{,}\) we can graph the line using slope triangles:

Compared with the intercepts method, the slope triangle method takes more time, but shows more points with slope triangles, and thus a more accurate graph. Also sometimes (as with Example 4.7.14) when we graph a standard form equation like \(2x-3y=0\text{,}\) the intercepts method doesn't work because both intercepts are actually at the same point, and we have to resort to something else like slope triangles anyway.