Question

Select the correct statement about the function represented by the table.

1 26 2 44 3 62 4 80 5 98

A. It is an exponential function because the factor between each x-
and y-value is constant.
O
B. It is a linear function because the y-values increase by an equal
difference over equal intervals of x-values.
C. It is a linear function because the difference y - x for each row is
constant.
+ PREVIOUS​

Answer 1

Answer: C

Step-by-step explanation: it looks s a linear function because the y-values increase by an equal difference over equal intervals of x-values

Answer 2

Option "B. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values" is the correct answer

Explanation:

First of all we have to check the function for linear or exponential.

To check for exponential function, we have to find the factor between y values and x values that is:

`factor = (y)/(x)`

So,

For x=1

`(26)/(1) = 26\\(44)/(2) = 22\\(62)/(3) = 20.6`

The function is not an exponential function because the factor between each x-value and y-value is not same.

Now,

Let us find the difference between x-values and y-values

Let

`x_1 = 1\\x_2 = 2\\x_3 = 3\\x_4 = 4\\and\\y_1 = 26\\y_2 = 44\\y_3 = 62\\y_4 = 80`

So for x-values

`x_2-x_1 = 2-1 = 1\\x_3-x_2 = 3-2 = 1\\x_4 - x_3 = 4-3 = 1`

And

`y_2 - y_1 = 44-26 = 18\\y_3 - y_2 = 62-44 = 18\\.\\.\\.`

As we can see that the y-values increase by an equal difference over equal intervals of x-values so the function is a linear function.

Hence,

Option "B. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values" is the correct answer