Answer:
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
Step-by-step 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:
[tex]factor = \frac{y}{x}[/tex]
So,
For x=1
[tex]\frac{26}{1} = 26\\\frac{44}{2} = 22\\\frac{62}{3} = 20.6[/tex]
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
[tex]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[/tex]
So for x-values
[tex]x_2-x_1 = 2-1 = 1\\x_3-x_2 = 3-2 = 1\\x_4 - x_3 = 4-3 = 1[/tex]
And
[tex]y_2 - y_1 = 44-26 = 18\\y_3 - y_2 = 62-44 = 18\\.\\.\\.[/tex]
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
