SAT Mathematics Practice Test 5

he slope of a line is and can be calculated using the coordinates of any two points on the line. For example, the graph of $\mathit{f}$ passes through the points $\left(0,3\right)$ and $\left(2,4\right),$ so the slope of the graph of $\mathit{f}$ is $\frac{4-3}{2-0}=\frac{1}{2}$ . The slope of the graph of function $\mathit{g}$ is $4$ times the slope of the graph of f, so the slope of the graph of $\mathit{g}$ is $4\left(\frac{1}{2}\right)=2$ . Since the point $\left(0,-4\right)$ is the y-intercept of g, g is defined as $\mathit{g}\left(\mathit{x}\right)=2\mathit{x}-4.$ It follows that $\mathit{g}\left(9\right)=2\left(9\right)-4=14.$
Choice A is incorrect because if g(9) = 5, then the slope of the graph of function g is $\frac{-4-5}{0-9}=1$,which is not 4 times the slope of the graph of f. Choices B and D are also incorrect. The same procedures used to test choice A yields $\frac{-4-9}{0-9}=\frac{13}{9}$ and $\frac{-4-18}{0-9}=\frac{22}{9}$ for the slope of the graph of $\mathit{g}$ for choices B and D, respectively. Neither of these slopes is 4 times the slope of the graph of $\mathit{f}$