Extra explanation: zero | Wiskunde op Tilburg University

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

$(-\frac{b}{a},0)$ .