SAT Question ab7740a8: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Choice D is correct. The relationship between the values of $x$ and their corresponding $y$-values is nonlinear if the rate of change between these pairs of values isn't constant. The table for choice D gives four pairs of values: $(1,6)$, $(2,12)$, $(3,24)$, and $(4,48)$. Finding the rate of change, or slope, between $(1,6)$ and $(2,12)$ by using the slope formula, $\frac{y_2-y_1}{x_2-x_1}$, yields $\frac{12-6}{2-1}$, or $6$. Finding the rate of change between $(2,12)$ and $(3,24)$ yields $\frac{24-12}{3-2}$, or $12$. Finding the rate of change between $(3,24)$ and $(4,48)$ yields $\frac{48-24}{4-3}$, or $24$. Since the rate of change isn't constant for these pairs of values, this table shows a nonlinear relationship.