### 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 $$y = 2x + 1$$.

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.