SOLUTION: Determine whether the lines l1 and l2 are parallel, perpendicular, or neither. Line l1 goes through (3, –8) and (–3, 9). Line l2 goes through (–1, –5) and (–7, 12).

Algebra ->  Linear-equations -> SOLUTION: Determine whether the lines l1 and l2 are parallel, perpendicular, or neither. Line l1 goes through (3, –8) and (–3, 9). Line l2 goes through (–1, –5) and (–7, 12).       Log On


   

Question 150557: Determine whether the lines l1 and l2 are parallel, perpendicular, or neither.
Line l1 goes through (3, –8) and (–3, 9). Line l2 goes through (–1, –5) and (–7, 12).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the slope of the line through the points (3, -8) and (-3, 9).



m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%289--8%29%2F%28-3-3%29 Plug in y%5B2%5D=9, y%5B1%5D=-8, x%5B2%5D=-3, x%5B1%5D=3, ,


m=%2817%29%2F%28-3-3%29 Subtract -8 from 9 to get 17


m=%2817%29%2F%28-6%29 Subtract 3 from -3 to get -6


m=-17%2F6 Reduce


So the slope of the line that goes through the points and is m=-17%2F6


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Now let's find the slope of the line through the points (-1, -5) and (-7, 12).




m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2812--5%29%2F%28-7--1%29 Plug in y%5B2%5D=12, y%5B1%5D=-5, x%5B2%5D=-7, x%5B1%5D=-1, ,


m=%2817%29%2F%28-7--1%29 Subtract -5 from 12 to get 17


m=%2817%29%2F%28-6%29 Subtract -1 from -7 to get -6


m=-17%2F6 Reduce


So the slope of the line that goes through the points and is m=-17%2F6



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Since the slopes of the lines through both pairs of points are both m=-17%2F6, this means that the two slopes are equal. So this means that the two lines are parallel.


To verify this, we can simply graph the points and lines and we'll see that the two lines are parallel