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Which pair of equations represents parallel lines?

Rationale

x + 2y = 8 and -x - 2y = 3 represent parallel lines.

The equations of parallel lines share the same slope but have different y-intercepts. In this case, both equations can be manipulated to reveal that they have identical slopes, confirming their parallel nature.

A (-2x + y + 2 = 0, y = -(1/2)x - 4) YOUR ANSWER

To find the slope of the first equation, rearranging it gives y = 2x - 2, indicating a slope of 2. The second equation has a slope of -1/2. Since these slopes differ, the lines are not parallel.

B (3x + y = -8, y = 3x - 8) YOUR ANSWER

The first equation can be rearranged to y = -3x - 8, revealing a slope of -3. The second equation has a slope of 3. These slopes are not equal, indicating that these lines are not parallel.

C (x + 2y = 8, -x - 2y = 3) CORRECT

Rearranging the first equation yields y = -1/2x + 4, which has a slope of -1/2. The second equation rearranges to y = -1/2x - 3/2, also yielding a slope of -1/2. Since both equations share the same slope, they are indeed parallel lines.

D (-(2/3)x + y = 12, y = -(3/2)x - 1) YOUR ANSWER

The first equation rearranges to y = (2/3)x + 12, giving it a slope of 2/3. The second equation has a slope of -3/2. These different slopes indicate that the lines are not parallel.

Conclusion

For two lines to be parallel, they must possess identical slopes. In this case, option C demonstrates that both equations have the same slope of -1/2, confirming their parallel relationship. The other choices feature different slopes, which disqualifies them from being parallel lines.

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