Question

Which pair of lines is parallel?

A. y=4x+1 and y+4x=5
B. y=−2x+1 and 2y−2x=−2
C. −x+2 and y−2=−x+3
D. 5y+x=10 and y=3x+1

Answer 1

To find parallel lines, we compare the slopes of each line. Upon analyzing the given line pairs, none of them have equal slopes, and thus none of the pairs listed are parallel lines.

Step-by-step explanation:

To determine which pair of lines is parallel, we need to look at the slope of each line. Lines are parallel if they have the same slope. The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.

• Pair A: y = 4x + 1 and y + 4x = 5 can be rewritten as y = -4x + 5. These lines are not parallel as their slopes (4 and -4) are not equal.
• Pair B: y = -2x + 1 and 2y - 2x = -2 can be rewritten as y = x - 1. These lines are not parallel as their slopes (-2 and 1) are not equal.
• Pair C: -x + 2 and y - 2 = -x + 3 are not in slope-intercept form and cannot be directly compared, but upon rearranging, neither equation yields a slope-intercept form resembling y = mx + b and thus they do not describe lines.
• Pair D: 5y + x = 10 can be rewritten as y = -1/5x + 2 and y = 3x + 1 are not parallel as their slopes (-1/5 and 3) are not equal.

Therefore, none of the pairs listed are parallel lines.