SAT Mathematics Practice Test 2

In the $\mathit{x}\mathit{y}-$plane, the slope m of the line that passes through the points $\left({\mathit{x}}_1,{\mathit{y}}_1\right)$ and $\left({\mathit{x}}_2,{\mathit{y}}_2\right)$ is given by the formula $\mathit{m}=\frac{{\mathit{y}}_2-{\mathit{y}}_1}{{\mathit{x}}_2-{\mathit{x}}_1}$ Thus, if the graph of the linear function f has intercepts at $\left(\mathit{a},0\right)$ and $\left(0,\mathit{b}\right)$, then the slope of the line that is the graph of $\mathit{y}=\mathit{f}\left(\mathit{x}\right)$ is $\mathit{m}=\frac{0-\mathit{b}}{\mathit{a}-0}=-\frac{\mathit{b}}{\mathit{a}}$ It is given that a + b = 0, and so a = −b. Finally, substituting $-\mathit{b}$ for $\mathit{a}$ in m = −b/a gives $\mathit{m}=-\frac{\mathit{b}}{-\mathit{b}}=1,$ which is positive.
Choices B, C, and D are incorrect and may result from a conceptual misunderstanding or a calculation error.