Answer: y = 2x
There are infinitely many possible answers.
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Explanation:
- If m = 1, then y = mx+b would be perpendicular to the original equation. Recall that if two slopes multiply to -1, then the lines are perpendicular. So we ignore cases when m = 1.
- If m = -1, and b is nonzero, then y = mx+b is parallel to y = -x. Parallel lines have equal slopes and different y intercepts. We'll ignore m = -1 as well.
- If m is any other value, then y = mx+b will intersect y = -x exactly once. This is why we have infinitely many solutions. In the case of y = 2x, we have m = 2 and b = 0.
