Question

Which table represents a linear function?

Answer 1

Well, a linear function is proportional, a straight line (on a graph). And the numbers must not have the same answer. For instance, if the X input is 5, and the Y output is 7. And then another X input is 5, and the Y output is 8, that's non-linear.

So, the Answer would be the third graph. This is because the X values are steadily increasing, and so are the Y values. 

For the X and Y values, for each time X increases by 1, Y increases by -8. This is, linear because both sides are constantly and evenly increasing.

Answer 2

Table 3 represents the linear function.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Explanation:

In table 1,

The slope can be obtained as follows,

$\begin{aligned}m&=\frac{{ - 6 + 2}}{{2 - 1}}\\&=\frac{{ - 4}}{1}\\&= - 4\\\end{aligned}$

The slope of other two points can be obtained as follows,

$\begin{aligned}m&= \frac{{ - 2 + 6}}{{3 - 2}}\\&= \frac{4}{1}\\&=4\\\end{aligned}$

The slope is not equal. Therefore, table 1 is not correct.

In table 2,

The slope can be obtained as follows,

$\begin{aligned}m&= \frac{{ - 5 + 2}}{{2 - 1}}\\&=\frac{{ - 3}}{1}\\&= - 3\\\end{aligned}$

The slope of other two points can be obtained as follows,

$\begin{aligned}m&=\frac{{ - 9 + 5}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}$

The slope is not equal. Therefore, table 2 is not correct.

In table 3,

The slope can be obtained as follows,

$\begin{aligned}m&= \frac{{ - 10 + 2}}{{2 - 1}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}$

The slope of other two points can be obtained as follows,

$\begin{aligned}m&= \frac{{ - 18 + 10}}{{3 - 2}}\\&= \frac{{ - 8}}{1}\\&= - 8\\\end{aligned}$

The slopes are equal. Therefore, table 3 is correct.

In table 4,

The slope can be obtained as follows,

$\begin{aligned}m&= \frac{{ - 4 + 2}}{{2 - 1}}\\&=\frac{{ - 2}}{1}\\&= - 2\\\end{aligned}$

The slope of other two points can be obtained as follows,

$\begin{aligned}m&=\frac{{ - 8 + 4}}{{3 - 2}}\\&= \frac{{ - 4}}{1}\\&= - 4\\\end{aligned}$

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.