Which table represents the increasing linear function with the greatest unit rate? A. x y 2 16 5 10 B. x y 2 14 6 12C. x y 2 -24 5 -15 D. x y 2 -12 6 -16 E. x y 2 -19 6 -17

To find the linear function with the greatest unit rate, we need to calculate the rate of change (slope) of each of the given points. A. (2,16) and (5,10), Rate of change= [tex] \frac{10-16}{5-2}=\frac{-6}{3}= -2 [/tex]B. (2,14) and (6,12), Rate of change= [tex] \frac{12-14}{6-2}=\frac{-2}{4}=\frac{-1}{2} [/tex]C. (2,-24) and (5,-15), Rate of change=[tex] \frac{-15+24}{5-2}=\frac{9}{3}=3 [/tex]D. (2,-12) and (6,-16), Rate of change= [tex] \frac{-16+12}{6-2}=\frac{-4}{2}=-2 [/tex]E. (2,-19) and (6,-17), Rate of change=[tex] \frac{-17+19}{6-2}=\frac{2}{4}=\frac{1}{2} [/tex] Since, it can be seen that the greatest rate of change is 3 which is of the points given in Option C, therefore, it is the linear function with greatest unit rate(increasing).