Answer
$\displaystyle \frac{dy}{dx}=-\frac{2}{3}$
Work Step by Step
Differentiating an equation containing terms of form $f(x)$ and $g(y)$,
terms of the form $f(x)$ are differentiated directly, $\displaystyle \frac{d}{dx}[f(x)],$
and
terms of the form $g(y)$ are differentiated using the chain rule,
$\displaystyle \frac{d}{dx}[g(y)]=\frac{d}{dy}[g(y)]\cdot\frac{dy}{dx}$
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$\displaystyle \frac{d}{dx}(2x+3y)=\frac{d}{dx}(7)$
$2+3\displaystyle \frac{dy}{dx}=0$
$3\displaystyle \frac{dy}{dx}=-2$
$\displaystyle \frac{dy}{dx}=-\frac{2}{3}.$
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Alternatively, solving the initial equation for y:
$2x+3y=7\quad/-2x$
$3y=-2x+7\quad/\div 3$
$y=\displaystyle \frac{-2}{3}x+\frac{7}{3}$
Differentiating (constant multiple, constant),
$\displaystyle \frac{dy}{dx}=-\frac{2}{3}+0=-\frac{2}{3}$
