###### Example4.9.15

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 4.7.16) 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.

in-context