Introduction: A function of the form $y(x)=ax+b$, where $a$ and $b$ are numbers ($a\neq 0$),
is called a linear function.
Zero: To determine the point of intersection of the graph of a linear function $y(x)=ax+b$ with the $x$-axis, we calculate the zero of the function $y(x)$,
$$\begin{align}
y(x)=0 &\Leftrightarrow ax+b = 0\\
&\Leftrightarrow ax=-b\\
&\Leftrightarrow x=-\frac{b}{a}.
\end{align}$$
Since a linear function $y(x)=ax+b$ has precisely one zero, the graph has precisely one point of intersection with the $x$-axis. Hence, the point of intersection of the graph of a linear function and the $x$-axis is $(-\frac{b}{a},0)$.
Zero: To determine the point of intersection of the graph of a linear function $y(x)=ax+b$ with the $x$-axis, we calculate the zero of the function $y(x)$,
$$\begin{align}
y(x)=0 &\Leftrightarrow ax+b = 0\\
&\Leftrightarrow ax=-b\\
&\Leftrightarrow x=-\frac{b}{a}.
\end{align}$$
Since a linear function $y(x)=ax+b$ has precisely one zero, the graph has precisely one point of intersection with the $x$-axis. Hence, the point of intersection of the graph of a linear function and the $x$-axis is $(-\frac{b}{a},0)$.