Answer
$\text{Slope: }
-\dfrac{2}{7}
\\\text{$y$-intercept: }
\dfrac{1}{7}$
Work Step by Step
The given equation is equivalent to
\begin{array}{l}\require{cancel}
2x+7y=1
\\\\
7y=-2x+1
\\\\
\dfrac{7y}{7}=\dfrac{-2}{7}x+\dfrac{1}{7}
\\\\
y=-\dfrac{2}{7}x+\dfrac{1}{7}
.\end{array}
Using $y=mx+b$ (where $m$ is the slope and $b$ is the $y$-intercept) or the Slope-Intercept Form of linear equations, then the equation, $
y=-\dfrac{2}{7}x+\dfrac{1}{7}
,$ has the following properties:
\begin{array}{l}\require{cancel}
\text{Slope: }
-\dfrac{2}{7}
\\\text{$y$-intercept: }
\dfrac{1}{7}
.\end{array}