The following values of $x$ and $y$ are thought to satisfy a linear equation:

$x$	$1$	$2$
$y$	$1$	$3$

Draw the graph,using the values of $x, y$ as given in the above table.
At what point does the graph of the linear equation:
$(i)$ cut the $x$-axis?
$(ii)$ cut the $y$-axis?

(N/A) From the table,we get two points $A(1, 1)$ and $B(2, 3)$ which lie on the graph of the linear equation. Obviously,the graph will be a straight line. So,we first plot the points $A$ and $B$ and join them as shown in the figure.
To find the equation of the line passing through $(1, 1)$ and $(2, 3)$:
Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 1} = 2$.
Using the point-slope form $y - y_1 = m(x - x_1)$:
$y - 1 = 2(x - 1) \implies y - 1 = 2x - 2 \implies y = 2x - 1$.
$(i)$ To find where it cuts the $x$-axis,set $y = 0$:
$0 = 2x - 1 \implies 2x = 1 \implies x = \frac{1}{2}$.
So,it cuts the $x$-axis at the point $\left(\frac{1}{2}, 0\right)$.
$(ii)$ To find where it cuts the $y$-axis,set $x = 0$:
$y = 2(0) - 1 \implies y = -1$.
So,it cuts the $y$-axis at the point $(0, -1)$.