6. Parallel and Perpendicular Lines
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Parallel lines have the same slope and the slopes of perpendicular lines are opposite reciprocals.
Parallel: y=6x and y=6x-2
Perpendicular: y=- 1/6x and y=6x; y=- 1/6x and y=6x-2
Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we check if their slopes are opposite reciprocals. Let's tackle these questions one at a time.
| Option | Equation | Slope |
|---|---|---|
| (I) | y=-1/6x | -1/6 |
| (II) | y=6x | 6 |
| (III) | y=6x-2 | 6 |
Now that we've identified the slope of each line, we can see that (II) and (III) have the same slope, so they are parallel.
For lines with different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals -1 are opposite reciprocals, and therefore the lines are perpendicular. Let's calculate the product of - 16 and 6. -1/6* 6=- 1 Since the product equals - 1, line (I) is perpendicular to both lines (II) and (III).