Values given in the tables are of #x# and#f(x)# and there are four data points in each table, say #(x_1,f(x_1))#, #(x_2,f(x_2))#, #(x_3,f(x_3))# and #(x_4,f(x_4))#.
If for #color(red)("all data points, we have same")# value of #(f(x_i)-f(x_j))/(x_i-x_j)#, we say that table of values represents a linear function.
For example in Table A, we have
#(15-12)/(5-4)=3# but #(23.4375-18.75)/(7-6)=4.6875#, hence it is not linear.
In Table C, we have
#(11-10)/(2-1)=1# but #(10-11)/(3-2)=-1#, hence it is not linear.
In Table D, we have
#(8-6)/(2-1)=2# but #(6-4.5)/(1-0)=1.5#, hence it is not linear.
But in Table B, we have
#(24-15)/(7-4)=3# and so are #(30-24)/(9-7)=3# and #(48-30)/(15-9)=3#
Hence it is linear.
