SAT Mathematics Practice Test 6

n the xy-plane, the graph of the equation $\mathit{y}=\mathit{m}\mathit{x}+\mathit{b}$, where m and b are constants, is a line with slope m and y-intercept (0,b). Therefore, the graph of $\mathit{y}=2\mathit{x}-5$ in the xy-plane is a line with slope 2 and a y-intercept $\left(0,-5\right)$. Having a slope of 2 means that for each increase in x by 1, the value of y increases by 2. Only the graph in choice D has a slope of 2 and crosses the y-axis at $\left(0,-5\right).$ Therefore, the graph shown in choice D must be the correct answer. Choices A, B, and C are incorrect. The graph of $\mathit{y}=2\mathit{x}-5$ in the xy-plane is a line with slope 2 and a y-intercept at $\left(0,-5\right).$ The graph in choice A crosses the y-axis at the point $\left(0,2.5\right)$, not $\left(0,-5\right)$, and it has a slope of $\frac{1}{2}$, not 2. The graph in choice B crosses the y-axis at (0, −5); however, the slope of this line is −2, not 2. The graph in choice C has a slope of 2; however, the graph crosses the y-axis at $\left(0,5\right)$, not $\left(0,-5\right).$