Question

Draw a graph for the following table and identify the variation.

$x$	$2$	$3$	$5$	$8$	$10$
$y$	$8$	$12$	$20$	$32$	$40$

Hence, find the value of $y$ when $x=4$.

Answer 1

From the table, we found that as $x$ increases, $y$ also increases. Thus, the variation is a direct variation

Let $y=kx$

$\Rightarrow$ $\frac{y}{x}=k$

where $k$ is the constant of proportionality

From the given values, we have

$k=\frac{8}{2}=\frac{12}{3}=....=\frac{40}{10}$, $\because$ $k=4$

The relation $y=4x$ forms a straight line graph.

Plot the points $(2,8),(3,12),(5,20),(8,32)$ and $(10,40)$ and join these points to get the straight line

Clearly, $y=4x=16$ when $x=4$.