Example 2

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 $(-\frac{1}{3}, \frac{4}{3})$.