SOLUTION: A line k passes through the points ​(−5​,−8​) and ​(1,34​). A second line h passes through the points ​(−3​,−27​) and ​(3​,15​). Is line k parallel to

Algebra ->  Linear-equations -> SOLUTION: A line k passes through the points ​(−5​,−8​) and ​(1,34​). A second line h passes through the points ​(−3​,−27​) and ​(3​,15​). Is line k parallel to      Log On


   



Question 1203432: A line k passes through the points ​(−5​,−8​) and ​(1,34​). A second line h passes through the points ​(−3​,−27​) and ​(3​,15​). Is line k parallel to line​ h? Why or why​ not?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
How are the slopes for k and for h?

k
%2834%2B8%29%2F6
7

h
%2815%2B27%29%2F6
42%2F6
7

Both slopes the same. 7
so appear to be parallel.


You should also check to see if the two lines are or are not the same, just to be sure. (quick check the points with http://www.shodor.org/interactivate/activities/OrderedSimplePlot/ indicates not the same line)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A line k passes through the points ​(-5​,-8​) and ​(1,34​).
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-5, -8) and (x2, y2) = (1, 34).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2834--8%29%2F%281--5%29+=+7.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 7%2A-5+%2Bb+=+27. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-8-7%2A-5+=+27.

y=(7)x + (27)

Your graph:






line h passes through the points ​(-3​,-27%E2%80%8B) and ​(3%E2%80%8B,15​)
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-3, -27) and (x2, y2) = (3, 15).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%2815--27%29%2F%283--3%29+=+7.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 7%2A-3+%2Bb+=+-6. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-27-7%2A-3+=+-6.

y=(7)x + (-6)

Your graph:





so, a line k is y=7x+%2B+27+and a line h+is y=7x+-6
as you can see, both lines have same+slope, therefore lines are parallel

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+30%2C+7x+%2B+27%2C+7x+-6%29+