Let $A(a, 0)$ and $B(0, b)$ be two points on $x$ -axis and $y$ axis respectively


Given $(-5,4)$ divides line $A B$ in the ratio $1: 2$. By section formula we have
$$
\begin{aligned}
&-5=\frac{1 \times 0+2 \times a}{3} \\
\Rightarrow & a=\frac{-15}{2} \text { and } 4=\frac{1 \times b+2 \times 0}{3} \\
\Rightarrow & b=12
\end{aligned}
$$
Thus, $A=\left(\frac{-15}{2}, 0\right)$ and $B=(0,12)$
Hence, equation of line joining $\left(\frac{-15}{2}, 0\right)$ and $(0,12)$ is
$$
\begin{array}{l}
(y-0)=\frac{12-0}{0+\frac{15}{2}}\left(x+\frac{15}{2}\right) \\
\Rightarrow \quad y=\frac{4}{5}(2 x+15)
\end{array}
$$
$\Rightarrow 5 y=(8 x+60) \Rightarrow 8 x-5 y+60=0$