We determine the point of intersection of the graph of the function $y(x)=5x+3$ and the graph of the function $z(x)=-4x$.
$$\begin{align}
5x+3=-4x & \Leftrightarrow 9x+3=0\\
& \Leftrightarrow 9x=-3\\
& \Leftrightarrow x=-\frac{3}{9}\\
& \Leftrightarrow x=-\frac{1}{3}.
\end{align}$$
$z(-\frac{1}{3})=-4\cdot -\frac{1}{3} =\frac{4}{3}$. (Obviously, we also have $y(-\frac{1}{3})=5\cdot -\frac{1}{3}+3=\frac{4}{3}$.)
Consequently, the point of intersection is $(-\frac{1}{3}, \frac{4}{3})$.
$$\begin{align}
5x+3=-4x & \Leftrightarrow 9x+3=0\\
& \Leftrightarrow 9x=-3\\
& \Leftrightarrow x=-\frac{3}{9}\\
& \Leftrightarrow x=-\frac{1}{3}.
\end{align}$$
$z(-\frac{1}{3})=-4\cdot -\frac{1}{3} =\frac{4}{3}$. (Obviously, we also have $y(-\frac{1}{3})=5\cdot -\frac{1}{3}+3=\frac{4}{3}$.)
Consequently, the point of intersection is $(-\frac{1}{3}, \frac{4}{3})$.