SAT Mathematics Practice Test 6

According to the table, the value of y increases by $\frac{14}{4}=\frac{7}{2}$ value of x increases by 1. It follows that the simplest equation relating y to x is linear and of the form $\mathit{y}=\frac{7}{2}\mathit{x}+\mathit{b}$ for some constant b. Furthermore, the ordered pair $\left(1,\frac{11}{4}\right)$ from the table must satisfy this equation. Substituting 1 for x and $\frac{11}{4}$ for y in the equation $\mathit{y}=\frac{7}{2}\mathit{x}+\mathit{b}$ gives $\frac{11}{4}=\frac{7}{2}\left(1\right)+\mathit{b}$.solving for b gives $\mathit{b}=-\frac{3}{4}$.Therefore, the equation in choice D correctly relates y to x.
Choices A and B are incorrect. The relationship between x and y cannot be exponential because the differences, not the ratios, of y-values are the same every time the x-values change by the same amount. Choice C is incorrect because the ordered pair $\left(2,\frac{25}{4}\right)$ is not a solution to the equation $\mathit{y}=\frac{3}{4}\mathit{x}+2$.Substituting 2 for x and $\frac{25}{4}$ for y in this equation gives $\frac{25}{4}=\frac{3}{2}+2$.which is false.