Answer
Slope: $\dfrac{2}{7}$
$y$-intercept: $\dfrac{16}{7}$
$x$-intercept: $-8$
Work Step by Step
In the form $y=mx+b$, the given equation $
-2x+7y=16
,$ is equivalent to
\begin{align*}\require{cancel}
7y&=2x+16
\\\\
\dfrac{\cancel7y}{\cancel7}&=\dfrac{2x+16}{7}
\\\\
y&=\dfrac{2x}{7}+\dfrac{16}{7}
.\end{align*}
Since $m$ is the slope and $b$ is the $y$-intercept in $y=mx+b,$ then in the equation $y=\dfrac{2x}{7}+\dfrac{16}{7}$, the slope is $m=\dfrac{2}{7}$ and the $y$-intercept is $\dfrac{16}{7}$.
To find the $x$-intercept, set $y=0$ and solve for $x$ in the original equation. That is,
\begin{align*}\require{cancel}
-2x+7(0)&=16
\\
-2x+0&=16
\\
-2x&=16
\\\\
\dfrac{\cancel{-2}x}{\cancel{-2}}&=\dfrac{16}{-2}
\\\\
x&=-8
.\end{align*}
Hence, the $x$-intercept is $-8$.
