Answer
The graph is shown below.
Work Step by Step
The given linear equation is
$\Rightarrow -2x+7y=-21$
$x$ intercept.
Substitute $0$ for $y$.
$\Rightarrow -2x+7(0)=-21$
Simplify.
$\Rightarrow -2x=-21$
Divide each side by $-2$.
$\Rightarrow \frac{-2x}{-2}=\frac{-21}{-2}$
Simplify.
$\Rightarrow x=\frac{21}{2}$
The $x-$ intercept is $\frac{21}{2}$, so plot the point $(\frac{21}{2},0)$
$y$ intercept.
Substitute $0$ for $x$.
$\Rightarrow -2(0)+7y=-21$
Simplify.
$\Rightarrow 0+7y=-21$
$\Rightarrow 7y=-21$
Divide each side by $7$.
$\Rightarrow \frac{7y}{7}=\frac{-21}{7}$
Simplify.
$\Rightarrow y=-3$
The $y-$ intercept is $-3$, so plot the point $B=(0,-3)$
Draw a line through the points $A$ and $B$.
