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determine which two equations represent parallel lines
Each of those equations is in the slope-intercept form:
y = mx + b
where m represents the slope and (0,b) is the y-intercept.
Lines are parallel when and only when they have the same slope.
The slope is m, the coefficient of x.
Only the last two, y = 3x + 11 and y = 3x - 3 have the same
coefficient of x, or value of m, namely 3, and this is their
slope. So they are the only ones which are parallel.
Incidentally, the first two are perpendicular because they have
slopes which are negative reciprocals of each other, that is,
5/8 and -8/5