Question

Which table shows a linear function

Answer 1

Answer:

C. It is the THIRD box because it follows a constant rate of change in a linear path.

Answer 2

A linear function has a uniform rate of change (i.e. equal slopes).

The table that shows a linear function is table (3)

To do this, we simply calculate the slopes of each table, at different intervals

The slope is calculated using:

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

Table 1

Pick any two points

$(x_1,y_1) = (-5,-4)$

$(x_2,y_2) = (-3,-3)$

So, the slope is:

$m = \frac{-3--4}{-3--5}$

$m = \frac{1}{2}$

Pick another point on the table

$(x_2,y_2) = (1,2)$

Using the above point and $(x_1,y_1) = (-5,-4)$.

The slope (m) is:

$m = \frac{2 --4}{1--5}$

$m = \frac{6}{6}$

$m = 1$

The calculated slopes are not the same.

Hence, table 1 is not a linear function

Table 2

Pick any two points

$(x_1,y_1) = (-4,3)$

$(x_2,y_2) = (-3,0)$

So, the slope is:

$m = \frac{0-3}{-3--4}$

$m = \frac{-3}{1}$

$m =-3$

Pick another point on the table

$(x_2,y_2) = (-2,-1)$

Using the above point and $(x_1,y_1) = (-4,3)$

The slope (m) is:

$m = \frac{-1 -3}{-2--4}$

$m = \frac{-4}{2}$

$m =-2$

The calculated slopes are not the same.

Hence, table 2 is not a linear function

Table 3

Pick any two points

$(x_1,y_1) = (-5,-2)$

$(x_2,y_2) = (-3,0)$

So, the slope is:

$m = \frac{0--2}{-3--5}$

$m = \frac{2}{2}$

$m =1$

Pick another point on the table

$(x_2,y_2) = (-1,2)$

Using the above point and $(x_1,y_1) = (-5,-2)$

The slope (m) is:

$m = \frac{-2 -2}{-5--1}$

$m = \frac{-4}{-4}$

$m = 1$

The calculated slopes are the same.

Hence, table 3 is a linear function

Read more about linear functions at:

https://brainly.com/question/21107621