Prove and use slope criteria for parallel and perpendicular lines.
Decide whether two lines are parallel by comparing their slopes
Problem
Are \(\text{two}\) distinct lines with slopes \(3\) and \(3\) parallel?
Big Picture
What this problem is really about
Slope records direction, so parallelism is about equality of slopes rather than whether they are positive or negative. Confirm that the lines are distinct, compare the two slope values directly, and reserve the special vertical-line case for equations whose slopes are undefined.
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