Answer
$x=-5$, $y=-3$, see graph
Work Step by Step
Consider the given linear equation
$3x+5y+15=0$
Use intercepts to graph the given equation as follows:
Step 1: Find the $x$ intercept.
To find the x intercept of the line, substitute $y=0$ in the equation and calculate the value of x.
$\begin{align}
& 3x+5\times 0+15=0 \\
& 3x=-15 \\
& x=\frac{\left( -15 \right)}{3} \\
& =-5
\end{align}$
So, the $x$ intercept of equation $3x+5y+15=0$ is $-5$. Hence, the line passes through the point $\left( -5,0 \right)$.
Step 2: Find the $y$ intercept.
To calculate the y intercept of the line, substitute $x=0$ in the equation and calculate the value of y.
$\begin{align}
& 3\times 0+5y+15=0 \\
& 5y=-15 \\
& y=\frac{\left( -15 \right)}{5} \\
& =-3
\end{align}$
So, the $y$ intercept of the given equation $3x+5y+15=0$ is $-3$. Hence, the line passes through $\left( 0,-3 \right)$.
Step 3: Graph the equation of the straight line.
Locate the two intercepts $\left( -5,0 \right)$ and $\left( 0,-3 \right)$. Connect them by a straight line.
The graph of the given equation $3x+5y+15=0$ is as follows:
