Answer
Hence, the correct graph is $C.$
Work Step by Step
The given linear equation is
$\Rightarrow 5x+3y=-30$
$x$ intercept.
Substitute $0$ for $y$.
$\Rightarrow 5x+3(0)=-30$
Simplify.
$\Rightarrow 5x=-30$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=-\frac{30}{5}$
Simplify.
$\Rightarrow x=-6$
The $x-$ intercept is $-6$, so plot the point $A=(-6,0)$
$y$ intercept.
Substitute $0$ for $x$.
$\Rightarrow 5(0)+3y=-30$
Simplify.
$\Rightarrow 0+3y=-30$
$\Rightarrow 3y=-30$
Divide each side by $3$.
$\Rightarrow \frac{3y}{3}=\frac{-30}{3}$
Simplify.
$\Rightarrow y=-10$
The $y-$ intercept is $-10$, so plot the point $B=(0,-10)$
Draw a line through the points $A$ and $B$.
Hence, the correct graph is $C.$
