Question

Which option is true according to the given table and the statements?

$x$	$-4$	$-3$	$-2$	$1$	$0$
$y$	$11$	$9$	$7$	$5$	$3$

Statement A: The table represents a linear function.
Statement B: The function is $y=-2x+3$.

• A. Statement A and B both are false.
• B. Statement B is true
• C. Statement A is true
• D. Statement A and B both are true

Answer 1

The correct option is D Statement A and B both are true

We know,

• A function is said to be linear if it has a constant rate of change and the line is of the form $y=mx+b$.
• A linear function has a constant rate of change and the graph is a straight line.

Let’s plot the points from the table on the graph.


$\to$ We could see that the graph is a straight line.
$\to$ Rate of change is also constant.


$\to$ Therefore, the function is a linear function.
$\to$ So, statement A is true.

To identify the function, we need to find the slope of the data and the $y$-intercept.
$\to$ $y$-intercept refers to the output $\left(y\right)$ of the data when the input $\left(x\right)$ is $0$. From the table, we can see that when $x=0,y=3$. So, the $y$-intercept is $3$.

$\to$ If we consider the points $(-3,9)$ and $(-4,11)$, $slope=\frac{\left(Changeiny\right)}{\left(Changeinx\right)}=\frac{9-11}{-3-(-4)}=\frac{9-11}{-3+4}=\frac{-2}{1}=-2$

$\to$ So the function is given by:
$y=\left(Slope\right)x+y$-intercept $=-2x+3$
$y=-2x+3$, which is the same as the equation of the function given in statement B.

Hence, statements A and B both are true.