Answer
$\text{slope: }
-\dfrac{2}{7}
\\\text{$y-$intercept: }
\dfrac{3}{2}
$
Work Step by Step
Using the properties of equality, the given equation, $
4x+14y=21
,$ is equivalent to
\begin{array}{l}
14y=-4x+21
\\\\
y=-\dfrac{4}{14}x+\dfrac{21}{14}
\\\\
y=-\dfrac{2}{7}x+\dfrac{3}{2}
.\end{array}
Using $y=mx+b$ (or the Slope-Intercept Form), where $m$ is the slope and $b$ is the $y-$intercept, then the equation above has the following characteristics:
\begin{array}{l}
\text{slope: }
-\dfrac{2}{7}
\\\text{$y-$intercept: }
\dfrac{3}{2}
.\end{array}