Question

Draw the graph for each equation given below; hence find the co-ordinates of the points where the graph drawn meets the co-ordinate axes:
$\frac{2x+15}{3}=y-1$.

Answer 1

$\frac{2x+15}{3}=y-1$
$\Rightarrow 2x+15=3(y-1)$
$\Rightarrow 2x+15=3y-3$
$\Rightarrow 2x-3y=-15-3$
$\Rightarrow 2x-3y=-18$
$\Rightarrow -3y=-18-2x$
$\Rightarrow y=\frac{-18-2x}{-3}$
When $x=0,y=\frac{-18-[2\times 0]}{-3}=\frac{-18-0}{-3}=6$
When $x=-3,y=\frac{-18-[2\times (-3\left)\right]}{-3}=\frac{-18+6}{-3}=4$
When $x=-6,y=\frac{-18-[2\times (-6\left)\right]}{-3}=\frac{-18+13}{-3}=2$

$x$	$0$	$-3$	$-6$
$y$	$6$	$4$	$2$

Hence, the graph meets the coordinate axes at $(-9,0)$ and $(0,6)$.