Answer
$\text{slope: }
-\dfrac{1}{4}
\\\text{$y-$intercept: }
\dfrac{2}{3}
$
Work Step by Step
Using the properties of equality, the given equation, $
3x+12y=8
,$ is equivalent to
\begin{array}{l}
12y=-3x+8
\\\\
y=-\dfrac{3}{12}x+\dfrac{8}{12}
\\\\
y=-\dfrac{1}{4}x+\dfrac{2}{3}
.\end{array}
Using $y=mx+b$, where $m$ is the slope and $b$ is the $y-$intercept, then the equation, $
y=-\dfrac{1}{4}x+\dfrac{2}{3}
,$ has the following characteristics:
\begin{array}{l}
\text{slope: }
-\dfrac{1}{4}
\\\text{$y-$intercept: }
\dfrac{2}{3}
.\end{array}
