Question

Line m passes through the points (-4, -11) and (3, 3). Line n passes through the points (5, -2) and (-6, 9). Which of the following explains whether lines m and n intersect?
Yes, lines m and n intersect because their slopes are different.
No, lines m and n never intersect because their slopes are the same.
No, lines m and n never intersect because their slopes are different.
Yes, lines m and n intersect because their slopes are the same.

Answer 1

Compute slopes.

Line m: slope = (3 - (-11)) / (3 - (-4)) = 14/7 = 2.
Line n: slope = (9 - (-2)) / (-6 - 5) = 11/(-11) = -1.

Since the slopes are different, the lines intersect. (Equations: m: y = 2x - 3, n: y = -x + 3; they meet at (2, 1).)

So the correct choice is: "Yes, lines m and n intersect because their slopes are different."