Question

Line m passes through points (4, 1) and (8, 3). Line n passes through points (−8, 1) and (4, 7). Are lines m and n parallel?

A) Yes, the lines are parallel because they have different slopes.
B) Yes, the lines are parallel because they have the same slope.
C) No, the lines are not parallel because they have different slopes.
D) No, the lines are not parallel because they have the same slope.

Answer 1

To determine if two lines are parallel, compare their slopes. Lines m and n have the same slope, so they are parallel.

Step-by-step explanation:

To determine if two lines are parallel, we need to compare their slopes. The slope of a line can be found using the formula: Slope = (change in y)/(change in x). For line m, the change in y is 3 - 1 = 2, and the change in x is 8 - 4 = 4. So the slope of line m is 2/4 = 1/2. For line n, the change in y is 7 - 1 = 6, and the change in x is 4 - (-8) = 12. So the slope of line n is 6/12 = 1/2. Since both lines have the same slope, we can conclude that lines m and n are parallel.