Question

For the data in the table, tell whether $y$ varies directly with $x$.

If it does, write an equation for the direct variation.

$x$	$0$	$1$	$2$	$3$
$y$	$0$	$4$	$8$	$12$

• A. No
• B. Yes, $y=4x$
• C. Yes, $y=0.25x$
• D. yes, $y=x+4$

Answer 1

The correct option is B

Yes, $y=4x$

Find whether $x$ and $y$ are in direct variation:

Explanation for the correct option:

Option $B$: Yes, $y=4x$

$x$	$0$	$1$	$2$	$3$
$y$	$0$	$4$	$8$	$12$

Direct Variation means when $y$ can be expressed as the product of some constant number $k$ and $x$.

$y=kx$

Here, if $x=1$ and $y=4$, then the value of $k$ can be calculated by $y=kx$.

$$\begin{gathered} y=kx \\ 4=k\left(1\right) \\ k=4 \end{gathered}$$

Put $x=2$ and $y=8$ in $y=kx$, the obtained value of $k$ is $4$.

Hence, $x$ and $y$ are in direct variation, and the equation for this is $y=4x$.

Hence, option $B$ is correct.

Explanation for incorrect options:

Option $A$: No

Since $x$ and $y$ are in direct variation and do not match with the calculated answer.

Hence, option $A$ is incorrect.

Option $C$: Yes, $y=0.25x$

This equation does not match the calculated equation.

Hence, option $C$ is incorrect.

Option $D$: Yes, $y=x+4$

This equation does not match the calculated equation.

Hence, option $D$ is incorrect.

Hence, option $B$ is correct.