Question

Please answer fast!

Which of the following tables represents a linear function?


x −4 −2 0 2 4
y negative three halves 0 1 5 over 2 4

x −3 −2 0 2 3
y 2 1 −1 1 2

x −3 −1 1 3 5
y 5 13 over 3 11 over 3 3 7 over 3

x 2 2 2 2 2
y −2 −1 0 1 2

Answer 1

Table 3 represents a linear function.

How to determine the table that represents a linear function?

In a linear function, the change in the y-value is proportional to the change in the x-value by a constant rate, known as the slope. We can calculate the slope of Table 3 by selecting any two points and using the formula:

slope = (y2 - y1) / (x2 - x1)

For example, if we choose the points (-2, -4) and (2, 0), we get:

slope = (0 - (-4)) / (2 - (-2)) = 4 / 4 = 1

This means that for every increase of 1 in the x-value, the y-value increases by 1. We can confirm that this holds for all the other points in Table 3 as well, indicating that it represents a linear function.

The other tables do not represent linear functions because the change in the y-value is not proportional to the change in the x-value at a constant rate.