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Determine which lines, if any, are parallel or perpendicular. Explain.

Line a: 2x - 7y = 14
Line b: y = 7/2x - 8
Line c: 2x + 7y = -21

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Final answer:

Lines a and c are neither parallel nor perpendicular, and Lines a and b are perpendicular. No lines are parallel.

Step-by-step explanation:

To determine if the lines are parallel or perpendicular, we need to put each equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Two lines are parallel if they have the same slope, and they are perpendicular if the product of their slopes is -1.

Line a: 2x - 7y = 14 can be rewritten as y = (2/7)x - 2. So, the slope of Line a is 2/7.
Line b is already in slope-intercept form: y = (7/2)x - 8. The slope of Line b is 7/2.
Line c: 2x + 7y = -21 can be rewritten as y = -(2/7)x - 3. The slope of Line c is -2/7.

Lines with slopes of 2/7 and -2/7 are neither parallel nor perpendicular because the slopes are neither equal nor negative reciprocals of each other. The lines with slopes of 2/7 and 7/2 are perpendicular since (2/7) * (7/2) = 1. There are no lines that are parallel in this set.

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