As the tables are not attached, the attachment is given below:
Answer:
Only table 3 represents the linear function.
Step-by-step explanation:
The linear equation with slope 'm' and intercept 'c' is given as:
[tex]y = mx + c[/tex]
The slope of a line with points [tex]\left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}} \right)[/tex] is given as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Table 1:
The slope is calculated as below:
[tex]\begin{aligned}m&=\frac{{ - 6 + 2}}{{2 - 1}}\\&=\frac{{ - 4}}{1}\\&= - 4\\\end{aligned}[/tex]
The slope of other two points can be obtained as follows,
[tex]\begin{aligned}m&= \frac{{ - 2 + 6}}{{3 - 2}}\\&= \frac{4}{1}\\&=4\\\end{aligned}[/tex]
The slopes are not equal. Therefore, table 1 is not correct.
Table 2:
The slope is calculated as below:
[tex]\begin{aligned}m&= \frac{{ - 5 + 2}}{{2 - 1}}\\&=\frac{{ - 3}}{1}\\&= - 3\\\end{aligned}[/tex]
The slope of other two points can be obtained as follows,
[tex]\begin{aligned}m&=\frac{{ - 9 + 5}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}[/tex]
The slopes are not equal. Therefore, table 2 is not correct.
Table 3:
The slope is calculated as below:
[tex]\begin{aligned}m&= \frac{{ - 10 + 2}}{{2 - 1}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}[/tex]
The slope of other two points can be obtained as follows,
[tex]\begin{aligned}m&= \frac{{ - 18 + 10}}{{3 - 2}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}[/tex]
The slopes are equal. Therefore, table 3 is correct.
Table 4:
The slope is calculated as below:
[tex]\begin{aligned}m&= \frac{{ - 4 + 2}}{{2 - 1}}\\&=\frac{{ - 2}}{1}\\&= - 2\\\end{aligned}[/tex]
The slope of other two points can be obtained as follows,
[tex]\begin{aligned}m&=\frac{{ - 8 + 4}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}[/tex]
The slopes are not equal. Therefore, table 4 is not correct.
Therefore, only table 3 represents the linear function.
