SAT Mathematics Practice Test 5

The equation $-2x+3y=6$ can be rewritten in the slope-intercept form as follows: $y = \frac{2}{3}x + 2$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 $m$ is the slope of a line perpendicular to the line with equation $y = \frac{2}{3}x + 2,$ then $m \times \frac{2}{3} = -1$ which yields $m = -\frac{3}{2}$.. Of the given choices, only the equation in choice A can be rewritten in the form $y = \frac{3}{2}x + b,$ 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 $-\frac{3}{2}$