Question

The table shows a function. Is the function linear or nonlinear?

$x$	$y$
$2$	6
3	10
5	12

• A. linear
• B. nonlinear

Answer 1

The correct option is B nonlinear

If the rate of change of a function is the same between any two points, then it is linear; otherwise, it is nonlinear.

A function's rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $\frac{y_2-y_1}{x_2-x_1}$

Let's find the rate of change:

$x$	$y$
$2$	6
3	10
5	12

Row 1 and 2:

Rate of chage between $(2,6)$ and $(3,10)$
$=\frac{10-6}{3-2}$
$=\frac{4}{1}$
$=4$

Row 2 and 3:

Rate of chage between $(3,10)$ and $(5,12)$
$=\frac{12-10}{5-3}$
$=\frac{2}{2}$
$=1$

Clearly, rate of change between $(3,10)$ and $(5,12)\ne$ rate of chage between $(2,6)$ and $(3,10)$

Hence, the function is nonlinear.