Is the relationship shown by the data linear? If so, model the data with an equation. X Y3 17 211 318 5A. The relationship is linear; y-2= 1/4 (x + 7)B.The relationship is linear; y+2 = -1/4 (X - 7)C.The relationship is not linear.D. The relationship is linear; y+2= 1/4 (X - 7)

Accepted Solution

Answer:  C.  The relationship is not linear. Step-by-step explanation:When the rate of change  is constant of one variable is corresponding to the change in the other variable , then the relationship is said to be linear.The rate of change is given by:-[tex]R=\frac{\text{change in y}}{\text{change in x}}\\\Rightarrow\ R=\frac{2-1}{7-3}=\frac{1}{4}[/tex]Also, [tex]\\\Rightarrow\ R=\frac{5-3}{18-11}=\frac{2}{7}[/tex] [tex]But\ \frac{1}{4}\neq\frac{2}{7}[/tex]Therefore, the rate of change is not constant .Hence, The relationship is not linear.