The equation
−2x+3y=6 can be rewritten in the slope-intercept form as follows:
y=x+2So the slope of the graph of the given equation is
. 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=x+2, then
m×=−1 which yields
m=−.. Of the given choices, only the equation in choice A can be rewritten in the form
y=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
−,−, and
−, not
−