Question

which table represents a linear function?
1.

$x$	$y$
2	7
3	11
4	15

2.

$x$	$y$
2	6
3	15
4	31

3.

$x$	$y$
2	9
3	3
4	9

4.

$x$	$y$
2	9
3	27
4	81

Explanation:

Step1: Recall linear function rule

A linear function has a constant rate of change (slope) between $x$ and $y$, meaning the difference in $y$-values is the same for each equal increase in $x$-values.

Step2: Check Table 1

Calculate $\Delta y$ for each $\Delta x=1$:
$7-3=4$, $11-7=4$, $15-11=4$
Constant $\Delta y=4$

Step3: Check Table 2

Calculate $\Delta y$ for each $\Delta x=1$:
$6-3=3$, $15-6=9$, $31-15=16$
$\Delta y$ is not constant

Step4: Check Table 3

Calculate $\Delta y$ for each $\Delta x=1$:
$9-3=6$, $3-9=-6$, $9-3=6$
$\Delta y$ is not constant

Step5: Check Table 4

Calculate $\Delta y$ for each $\Delta x=1$:
$9-3=6$, $27-9=18$, $81-27=54$
$\Delta y$ is not constant

Answer:

The first table (with $x$: 1,2,3,4 and $y$: 3,7,11,15) represents a linear function.