Question

Choose the correct answer for the given question:

Which rule represents the relation in the table $?$

$x$	$2$	$3$	$4$	$5$	$6$
$y$	$1$	$3$	$5$	$7$	$9$

• A. $y=x-1$
• B. $y=x+3$
• C. $y=2x-3$
• D. $y=2x=3$

Answer 1

The correct option is C

$y=2x-3$

Explanation for the correct option:

Option $\text{C}$: $y=2x-3$.

On putting $x=2$ in the given equation, we get $$\begin{gathered} y=2\left(2\right)-3 \\ y=4-3 \\ \mathbf{\text{y = 1}} \end{gathered}$$

On putting $x=3$ in the given equation, we get $$\begin{gathered} y=2\left(3\right)-3 \\ y=6-\text{3} \\ \mathbf{\text{y = 3}} \end{gathered}$$

On putting $x=4$ in the given equation, we get $$\begin{gathered} y=2\left(4\right)-3 \\ y=8-3 \\ \mathbf{\text{y = 5}} \end{gathered}$$

On putting $x=5$ in the given equation, we get $$\begin{gathered} y=2\left(5\right)-3 \\ y=10-3 \\ \mathbf{\text{y = 7}} \end{gathered}$$

On putting $x=6$ in the given equation, we get $$\begin{gathered} y=2\left(6\right)-3 \\ y=12-3 \\ \mathbf{\text{y = 9}} \end{gathered}$$

Explanation for the incorrect answers:

Option A: $y=x-1$

Here, when we put $x=3$, $y$ becomes $2$ which is not in the respective column of the given table.

Option B: $y=x+3$

Here, when we put $x=2$, $y$ becomes $5$ which is not in the respective column of the given table.

Option D: $y=2x+3$

Here, when we put $x=2$, $y$ becomes $7$ which is not in the respective column of the given table.

Hence, the correct option is C