How do I determine if this is a linear function?

Question

x values are : 3,5,6,8

y values are : 14,19,21.5,26.5

( in my book these values are in a table ) 

 

I tried to find the slope of (3,14) (5,19) (6,21.5) ( 8,26.5). The slopes weren't constant so doesn't that mean it's not a linear function ? My book says the answer is yes it's a linear function so I'm not sure. 

 

My my other two questions is a) Find f(2) and b) find x if f(x) =17.5 

 

 

 

the function of ion of the table of values is y= f(x)

Answer 1

If you calculate the change in y ÷ change in x for any pair of selected point (entries in your table) you will find that the slope comes out to 5/2, or 2.5.  So it's a linear function.  y = 2.5x + b; substituting (3,14) enables us to solve for b = 6.5.

 

Now you can say y = f(x) & f(2) = 2.5(2) + 6.5 = 11.5.