Table 3 represents the linear function.
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Explanation:
In table 1,
The slope can be obtained as follows,
[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 slope is not equal. Therefore, table 1 is not correct.
In table 2,
The slope can be obtained as follows,
[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 slope is not equal. Therefore, table 2 is not correct.
In table 3,
The slope can be obtained as follows,
[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.
In table 4,
The slope can be obtained as follows,
[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 slope is not equal. Therefore, table 4 is not correct.
Table 3 represents the linear function.
Learn more:
1. Learn more about line segment https://brainly.com/question/909890.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about coplanar and noncollinear https://brainly.com/question/4165000.
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: linear function, numbers, slope intercept, inequality, equation, y-intercept, graph, representation.
