Question

Determine if lines r and s are parallel.

A. The slope of line r is 2, and the slope of line s is -2. Since the slopes are different, lines r and s are not parallel.
B. Since both lines have a slope of 1/2, lines r and s are parallel.
C. The slope of line r is 2, and the slope of line s is -1/2. Since the product of their slopes is -1, lines r and s are parallel.
D. The slope of line r is 2, and the slope of line s is 2. Since the product of their slopes is not -1, lines r and s are not parallel.

Answer 1

The correct answer to whether lines r and s are parallel is B, since both lines have a slope of 1/2. This means they have identical slopes and are thus parallel to each other.

Step-by-step explanation:

To determine if lines r and s are parallel, we must compare their slopes. Parallel lines have identical slopes, meaning they rise and run at the same rate without intersecting. Looking at the multiple-choice options, the correct answer is B. Since both lines have a slope of ½, lines r and s are parallel. Confirming this, whenever two lines have the same slope and different y-intercepts, they run alongside each other infinitely without ever crossing.

Choice A is incorrect because a slope of 2 and a slope of -2 indicate that one line is rising while the other is falling, hence they are not parallel. Choice C is also incorrect; a product of slopes being -1 specifically indicates that the lines are perpendicular, not parallel. Finally, Choice D is incorrect because a slope of 2 for both lines does indeed mean they are parallel, which contradicts the statement provided in that option.