SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 through (–4, –7) and (1, 3) L2 through (2, 6) and (4, 10)

Algebra ->  Graphs -> SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 through (–4, –7) and (1, 3) L2 through (2, 6) and (4, 10)       Log On


   

Question 127128: Are the following lines parallel, perpendicular, or neither?
L1 through (–4, –7) and (1, 3)
L2 through (2, 6) and (4, 10)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope through (-4, -7) and (1, 3)

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Let's denote the first point (-4,-7) as . In other words, and

Now let's denote the second point (1,3) as . In other words, and



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

m=%283--7%29%2F%281--4%29 Plug in y%5B2%5D=3,y%5B1%5D=-7,x%5B2%5D=1,x%5B1%5D=-4


m=10%2F5 Subtract the terms in the numerator 3--7 to get 10. Subtract the terms in the denominator 1--4 to get 5

m=2 Reduce


So the slope of the line through the points (-4,-7) and (1,3) is m=2


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Now let's find the slope through (2, 6) and (4, 10)




Let's denote the first point (2,6) as . In other words, and

Now let's denote the second point (4,10) as . In other words, and



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

m=%2810-6%29%2F%284-2%29 Plug in y%5B2%5D=10,y%5B1%5D=6,x%5B2%5D=4,x%5B1%5D=2


m=4%2F2 Subtract the terms in the numerator 10-6 to get 4. Subtract the terms in the denominator 4-2 to get 2

m=2 Reduce


So the slope of the line through the points (2,6) and (4,10) is m=2


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Since the slope through the two pairs of points is m=2, this means that the two lines are parallel