SOLUTION: 1) Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l. a) 7/2 b)3 c)2/7 d)Undefined 2)Line l goes through the point (5

Algebra ->  Linear-equations -> SOLUTION: 1) Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l. a) 7/2 b)3 c)2/7 d)Undefined 2)Line l goes through the point (5      Log On


   

Question 102657: 1) Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l.
a) 7/2 b)3 c)2/7 d)Undefined

2)Line l goes through the point (5,-2) and is parpendicular to the line through (-2,1) and (-4,-2). Find the slope of l.
a) -2/3 b)-3/2 c)7/3 d)0

Any help anyone can provide with the above would great. I am trying to understand how to solves these. Thank you so much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1)
First find the slope through (4,3) and (-3,1)

Solved by pluggable solver: Finding the slope


Slope of the line through the points (4, 3) and (-3, 1)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%281+-+3%29%2F%28-3+-+4%29


m+=+%28-2%29%2F%28-7%29


m+=+2%2F7



Answer: Slope is m+=+2%2F7




Since the slope of the two lines are parallel, the slope of the unknown line through (1,3) is m=2%2F7. So the answer is C




2)

First find the slope through (-2,1) and (-4,-2)


Solved by pluggable solver: Finding the slope


Slope of the line through the points (-2, 1) and (-4, -2)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+%28x%5B1%5D%29%29


m+=+%28-2+-+1%29%2F%28-4+-+%28-2%29%29


m+=+%28-2+-+1%29%2F%28-4+%2B+2%29


m+=+%28-3%29%2F%28-2%29


m+=+3%2F2



Answer: Slope is m+=+3%2F2





Now to find the perpendicular slope, simply find the negative reciprocal of 3%2F2. To find the reciprocal, simply flip the fraction 3%2F2 to get 2%2F3. Now negate 2%2F3 to get -2%2F3.


So the perpendicular slope is -2%2F3 which means the answer is A