Question

if two lines are parallel, what must be true about their slopes?

a. they must be different.

b. they must be the same.

c. one of them must be zero.

d. they must be negative reciprocals.

Explanation:

To determine the relationship between the slopes of two parallel lines, we recall the geometric property of parallel lines in the context of linear equations (in the form \(y = mx + b\), where \(m\) is the slope). Parallel lines never intersect and have the same "steepness" and direction. This means their slopes must be equal.

• Option a is incorrect because different slopes would mean the lines are not parallel (they would intersect at some point).
• Option c is incorrect because only horizontal lines have a slope of zero, and not all parallel lines are horizontal.
• Option d is incorrect because negative reciprocals of slopes are the property of perpendicular lines (lines that intersect at a right angle), not parallel lines.

Answer:

b. They must be the same.