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:
$\frac{1}{3}x+\frac{1}{5}y=1$.

Answer 1

$\frac{1}{3}x+\frac{1}{5}y=1$
$\Rightarrow \frac{5x+3y}{15}=1$
$\Rightarrow 5x+3y=15$
$\Rightarrow 3y=15-5x$
$\Rightarrow y=\frac{15-5x}{3}$
When $x=0;y=\frac{15-5\times 0}{3}=\frac{15-0}{3}=5$
When $x=3;y=\frac{15-5\times 3}{3}=\frac{15-15}{3}=0$
When $x=-3;y=\frac{15-5\times (-3)}{3}=\frac{15+15}{3}=10$

$x$	$0$	$3$	$-3$
$y$	$5$	$0$	$10$

Plotting these points we get the required graph as shown below:
Hence, the graph meets the coordinate axes at $(3,0)$ and $(0,5)$.