SAT Mathematics Practice Test 5

The equation $-2\mathit{x}+3\mathit{y}=6$ can be rewritten in the slope-intercept form as follows: $\mathit{y}=\frac{2}{3}\mathit{x}+2$So the slope of the graph of the given equation is $\frac{2}{3}$ . In the xy-plane, whentwo non vertical lines are perpendicular, the product of their slopes is $-1$. So, if $\mathit{m}$ is the slope of a line perpendicular to the line with equation $\mathit{y}=\frac{2}{3}\mathit{x}+2,$ then $\mathit{m}\times \frac{2}{3}=-1$ which yields $\mathit{m}=-\frac{3}{2}$.. Of the given choices, only the equation in choice A can be rewritten in the form $\mathit{y}=\frac{3}{2}\mathit{x}+\mathit{b},$ for some constant b. Therefore, the graph of the equation in choice A is perpendicular to the graph of the given equation.
Choices B, C, and D are incorrect because the graphs of the equations in these choices have slopes, respectively, of $-\frac{3}{4},-\frac{1}{2},$ and $-\frac{1}{3},$ not $-\frac{3}{2}$