Good question - like most involving coordinate geometry, too, you don't need to know too specific a rule on this one...you can get by using logic.
To find the y-intercept (where the line crosses the y axis), you need to test the equation for where x = 0 (with x at zero, that's the y-axis). So you'd set x equal to 0, which just negates the entire x term in any of the answer choices. Only B and E have the same y-intercept, y = -3, as the original, so A, C, and D are all incorrect.
Then you can test for a line that's perpendicular to the original. If you look, though, E has the same slope (2) as the original, so it won't intersect it - they'll keep running parallel to each other. Therefore, E is incorrect, and B is the last man standing. Since you've proven the others to be incorrect, you don't even need to plot B as a line or rely on the lesser-used rule for perpendicular lines. B must be correct.
Often times, coordinate geometry questions can look as though they're from another world and take you back to graphing calculators and 7am high school classes. Usually, however, you can get by without having to have memorized specific coordinate formulas and rules:
-The coordinate plane is full of right angles, so use your knowledge of right triangles to find lengths and areas
-Lines will intersect each other at the same point, so to find an intersection you can just use algebra to find where x=x and y=y
-Etc.
A good working knowledge of coordinate geometry can certainly be helpful, but really only the basics are required...trust yourself that you can break a lot of coordinate geometry problems down to basic geometry and algebra. In most cases, the coordinate plane and its right-angles-galore will work distinctly to your advantage even if the idea of "coordinate geometry" on the surface seems intimidating.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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