Could the table represent the values of a linear function? Give a formula if it could.

Question

Could the table represent the values of a linear function? Give a formula if it could.
t     3      7    19       21      26     41
Q 5.38 6.66 10.50 11.14 12.74 17.54

If the values could represent a linear function, enter the exact answer. If the values could not represent a linear function, enter NA.

Note that "Q=" is already provided. Do not include this in your submitted response to this question.
Q=

Answer 1

                             slope

   t        Q       (Q_n-Q_n-1)/(_nt-t_n-1)

___     ___        ___________
   3     5.38
   7     6.66            0.32

 19     10.5            0.32
 21   11.14            0.32
 26   12.74            0.32
 41   17.54            0.32

 

Yes this is a linear function.  It has a slope of 0.32, so the function has the form:  Q = 0.32t + b

     where b is the value of Q when t=0.

You may use any of the points to determine b.

      Q - Q_n = (0.32)(t-tn)

      Q - 5.38 = (0.32(t-3)

      Q = 5.38 + 0.32t - 0.96

      Q = 0.32t + 4.42