Two nonvertical lines are parallel if and only if which condition holds?

Two nonvertical lines are parallel if and only if which condition holds?

• A. If they have the same slope
• B. If they are both horizontal
• C. If they have opposite slopes
• D. If one passes through the origin

Answer: (C)

The idea being tested is that parallel nonvertical lines share the same incline. For nonvertical lines, the slope m captures how steep the line is. If two lines have the same slope, they rise and run at the same rate, so they point in the same direction and never meet (unless they are actually the same line, i.e., coincident). If the slopes differ, the lines will cross at exactly one point. So two nonvertical lines are parallel precisely when their slopes are equal. White-they aren’t constrained to be horizontal; that’s just the zero-slope case, which is included. A line passing through the origin has no bearing on parallelism, since position doesn’t affect direction.

The idea being tested is that parallel nonvertical lines share the same incline. For nonvertical lines, the slope m captures how steep the line is. If two lines have the same slope, they rise and run at the same rate, so they point in the same direction and never meet (unless they are actually the same line, i.e., coincident). If the slopes differ, the lines will cross at exactly one point.

So two nonvertical lines are parallel precisely when their slopes are equal. White-they aren’t constrained to be horizontal; that’s just the zero-slope case, which is included. A line passing through the origin has no bearing on parallelism, since position doesn’t affect direction.