Answer
$-\frac{4}{3}$
Work Step by Step
$4x+3y=7$
$3y=7-4x$
$y=\frac{7}{3}-\frac{4}{3}x$
The slope is the coefficient of x (in $y = mx + b$ form) and is the rise over the run (or the change in y over the change in x).
Now the coefficient of x is $-\frac{4}{3}$, so this is the slope.
