Theory:

A polynomial of the form \(ax + b\), \(a \neq 0\) is a linear polynomial.
 
The graph of a linear polynomial is a straight line.
 
Consider the graph of \(y = 2x + 1\).
 
\(x\)
\(-2\)
\(-1\)
\(0\)
\(1\)
\(2\)
\(2x + 1\)
\(2(-2) + 1\)
 
\(=\) \(- 4 + 1\)
 
\(=\) \(-3\)
\(2(-1) + 1\)
 
\(=\) \(- 2 + 1\)
 
\(=\) \(-1\)
\(2(0) + 1\)
 
\(=\) \(0 + 1\)
 
\(=\) \(1\)
\(2(1) + 1\)
 
\(=\) \(2 + 1\)
 
\(=\) \(3\)
\(2(2) + 1\)
 
\(=\) \(4 + 1\)
 
\(=\) \(5\)
\(y\) \(=\) \(2x + 1\)
\(-3\)
\(-1\)
\(1\)
\(3\)
\(5\)
 
Join the coordinates \((-2, -3)\), \((-1, -1)\), \((0, 1)\), \((1, 3)\) and \((2, 5)\) by a straight line so as to obtain the graph of \(y = 2x + 1\).
 
linear.png
 
 
It is observed that, the graph of the polynomial \(y = 2x + 1\) intersects the \(x\) \(-\) axis at the point \((- 0.5, 1)\).
 
Also by the definition, the zero of \(y = 2x + 1\) is given by \(x = \frac{-1}{2} = -0.5\).
 
Thus, we can say that the zero of a linear polynomial is the \(x\) \(-\) coordinate of the point where the graph of the polynomial intersects the \(x\) \(-\) axis.
 
In general, for a linear polynomial \(ax + b\), \(a \neq 0\), the graph of \(y = ax + b\) represents a straight line which intersects the \(x\) \(-\) axis exactly at the point \(\left(\frac{-b}{a}, 0\right)\).
The linear polynomial \(ax + b\), \(a \neq 0\), has exactly one zero namely \(\frac{-b}{a}\) which is the \(x\) \(-\) coordinate of the point where the graph of the polynomial intersects the \(x\) \(-\) axis.