SOLUTION: A line k passes through the points (4, 2) and (-4, and 4). A second line h passes through the points ( -8,1) and ( 8, -3). Is the line k parallel to line h? Why or why not?

Algebra ->  Points-lines-and-rays -> SOLUTION: A line k passes through the points (4, 2) and (-4, and 4). A second line h passes through the points ( -8,1) and ( 8, -3). Is the line k parallel to line h? Why or why not?      Log On


   

Question 772604: A line k passes through the points (4, 2) and (-4, and 4). A second line h passes through the points ( -8,1) and ( 8, -3). Is the line k parallel to line h? Why or why not?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
(I)
If slopes for k and h are equal, then k and h are parallel; but if all four given points are on the same line, then k and h are equal or, "congruent".

(II)
m%5Bk%5D=%284-2%29%2F%28-4-4%29=-%281%2F4%29
m%5Bh%5D=%28-3-1%29%2F%288-%28-8%29%29=-%284%2F16%29=-%281%2F4%29

(III)
Are these lines the same?
y=mx%2Bb
b=y-mx
The formula for b allows to quickly determine the y-intercept for a line from slope-intercept form. Pick any of the line's points.
k: b=2-%28-1%2F4%294=2%2B1=3
h: b=1-%28-1%2F4%29%28-8%29=1-2=-1

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h and k are different lines with the same slope, so THEY ARE PARALLEL.
h is y=-%281%2F4%29x-1 and k is y=-%281%2F4%29x%2B3
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