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

$x$	$6$	$-6$
$y$	$-2$	$6$

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

(N/A) To find the linear equation $ax + by = c$,we use the two given points $(6, -2)$ and $(-6, 6)$.
For $(6, -2)$: $6a - 2b = c$
For $(-6, 6)$: $-6a + 6b = c$
Adding the two equations: $4b = 2c \implies c = 2b$.
Substituting $c = 2b$ into the first equation: $6a - 2b = 2b \implies 6a = 4b \implies a = \frac{2}{3}b$.
Let $b = 3$,then $a = 2$ and $c = 6$. The equation is $2x + 3y = 6$.
Plot the points $(6, -2)$ and $(-6, 6)$ on a Cartesian plane and join them with a straight line.
$(i)$ To find the $x$-intercept,set $y = 0$: $2x + 3(0) = 6 \implies 2x = 6 \implies x = 3$. The graph cuts the $x$-axis at $(3, 0)$.
$(ii)$ To find the $y$-intercept,set $x = 0$: $2(0) + 3y = 6 \implies 3y = 6 \implies y = 2$. The graph cuts the $y$-axis at $(0, 2)$.