Question

It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
It is linear because the function is continuous.
It is nonlinear because the final cost is determined by multiplying each price tag by 0.75.
It is nonlinear because the price tag and final cost columns do not have the same common difference.

Answer 1

Correct answer: The first statement is true; the other three are false.

Why:
- True: "It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant." This describes a constant rate of change (slope). For a 25% discount final cost = 0.75 × price, so the slope is constant (0.75), which makes the relationship linear.
- False: "It is linear because the function is continuous." Continuity alone does not imply linearity — many nonlinear functions are continuous.
- False: "It is nonlinear because the final cost is determined by multiplying each price tag by 0.75." Multiplying by a constant produces a linear (proportional) function y = 0.75x.
- False: "It is nonlinear because the price tag and final cost columns do not have the same common difference." The requirement for linearity is a constant rate of change in y with respect to x, not that the numeric differences in the two columns be equal. If x increases by a fixed amount, y will increase by a fixed amount (0.75 times that), so it is linear.