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

Only the first statement is correct.

- 1 is correct: the relation f(price) = 0.75·price is linear because the ratio Δ(final cost)/Δ(price) is constant (the slope = 0.75).
- 2 is incorrect: continuity alone does not imply linearity (many continuous functions are nonlinear).
- 3 is incorrect: multiplying by 0.75 gives a linear function (a constant multiple), not a nonlinear one.
- 4 is incorrect as stated: the two columns need a constant ratio (slope), not the same numeric common difference. For example, price tags 10, 20, 30 give final costs 7.5, 15, 22.5 — the differences (10 vs 7.5) are not equal but are proportional (7.5 = 0.75·10).