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:
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
The slope of a line with points
is given as:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Table 1:
The slope is calculated as below:
![\begin{aligned}m&=\frac{{ - 6 + 2}}{{2 - 1}}\\&=\frac{{ - 4}}{1}\\&= - 4\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B%20-%206%20%2B%202%7D%7D%7B%7B2%20-%201%7D%7D%5C%5C%26%3D%5Cfrac%7B%7B%20-%204%7D%7D%7B1%7D%5C%5C%26%3D%20-%204%5C%5C%5Cend%7Baligned%7D)
The slope of other two points can be obtained as follows,
![\begin{aligned}m&= \frac{{ - 2 + 6}}{{3 - 2}}\\&= \frac{4}{1}\\&=4\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B%20-%202%20%2B%206%7D%7D%7B%7B3%20-%202%7D%7D%5C%5C%26%3D%20%5Cfrac%7B4%7D%7B1%7D%5C%5C%26%3D4%5C%5C%5Cend%7Baligned%7D)
The slopes are not equal. Therefore, table 1 is not correct.
Table 2:
The slope is calculated as below:
![\begin{aligned}m&= \frac{{ - 5 + 2}}{{2 - 1}}\\&=\frac{{ - 3}}{1}\\&= - 3\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B%20-%205%20%2B%202%7D%7D%7B%7B2%20-%201%7D%7D%5C%5C%26%3D%5Cfrac%7B%7B%20-%203%7D%7D%7B1%7D%5C%5C%26%3D%20-%203%5C%5C%5Cend%7Baligned%7D)
The slope of other two points can be obtained as follows,
![\begin{aligned}m&=\frac{{ - 9 + 5}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B%20-%209%20%2B%205%7D%7D%7B%7B3%20-%202%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%204%7D%7D%7B1%7D%5C%5C%26%3D%20-%204%5C%5C%5Cend%7Baligned%7D)
The slopes are not equal. Therefore, table 2 is not correct.
Table 3:
The slope is calculated as below:
![\begin{aligned}m&= \frac{{ - 10 + 2}}{{2 - 1}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B%20-%2010%20%2B%202%7D%7D%7B%7B2%20-%201%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%208%7D%7D%7B1%7D%5C%5C%26%3D%20-%208%5C%5C%5Cend%7Baligned%7D)
The slope of other two points can be obtained as follows,
![\begin{aligned}m&= \frac{{ - 18 + 10}}{{3 - 2}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B%20-%2018%20%2B%2010%7D%7D%7B%7B3%20-%202%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%208%7D%7D%7B1%7D%5C%5C%26%3D%20-%208%5C%5C%5Cend%7Baligned%7D)
The slopes are equal. Therefore, table 3 is correct.
Table 4:
The slope is calculated as below:
![\begin{aligned}m&= \frac{{ - 4 + 2}}{{2 - 1}}\\&=\frac{{ - 2}}{1}\\&= - 2\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B%20-%204%20%2B%202%7D%7D%7B%7B2%20-%201%7D%7D%5C%5C%26%3D%5Cfrac%7B%7B%20-%202%7D%7D%7B1%7D%5C%5C%26%3D%20-%202%5C%5C%5Cend%7Baligned%7D)
The slope of other two points can be obtained as follows,
![\begin{aligned}m&=\frac{{ - 8 + 4}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B%20-%208%20%2B%204%7D%7D%7B%7B3%20-%202%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%204%7D%7D%7B1%7D%5C%5C%26%3D%20-%204%5C%5C%5Cend%7Baligned%7D)
The slopes are not equal. Therefore, table 4 is not correct.
Therefore, only table 3 represents the linear function.