Question

Which of the following answer choices

lists a pair of parallel lines?

A. y = x+3, y = x+5
B. y = 6x + 4, y = 2x +2
C. y = -5x -11, y = 5
D. y=-x-2, y = x+5

Answer 1

The pair of parallel lines listed is A. y = x + 3 and y = x + 5, as they have the same slope (m = 1) but different y-intercepts.

Step-by-step explanation:

The question asks to identify which option lists a pair of parallel lines. Two lines are considered parallel if they have the same slope but different y-intercepts. We can determine the slope of a line in the slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.

• y = x + 3 (slope m = 1)
• y = x + 5 (slope m = 1)
• y = 6x + 4 (slope m = 6)
• y = 2x + 2 (slope m = 2)
• y = -5x - 11 (slope m = -5)
• y = 5 (slope m = 0, since this is a horizontal line)
• y = -x - 2 (slope m = -1)
• y = x + 5 (slope m = 1)

The only pair with the same slope but different y-intercepts is A. y = x + 3 and y = x + 5. Thus, these are the pair of parallel lines.