SAT Mathematics Practice Test 5

he slope of a line is $\text{rise}/\text{run}$ and can be calculated using the coordinates of any two points on the line. For example, the graph of $f$ passes through the points $(0,3)$ and $(2,4),$ so the slope of the graph of $f$ is $\frac{4-3}{2-0}=\frac{1}{2}$ . The slope of the graph of function $g$ is $4$ times the slope of the graph of f, so the slope of the graph of $g$ is $4\left(\frac{1}{2}\right)=2$ . Since the point $(0,-4)$ is the y-intercept of g, g is defined as $g(x)=2x-4.$ It follows that $g(9)=2(9)-4=14.$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 $g$ for choices B and D, respectively. Neither of these slopes is 4 times the slope of the graph of $f$