SOLUTION: Find an equation of the line containing the given pair of points. (1/6, -1/3) and (5/6, 3)

Question 169006: Find an equation of the line containing the given pair of points.
(1/6, -1/3) and (5/6, 3)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find an equation of the line containing the given pair of points.
(1/6, -1/3) and (5/6, 3)
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The best method is determinants:
|x y 1|
|1/6 -1/3 1| = 0
|5/6 3 1|
x(-1/3 - 3) - y(1/6 - 5/6) + (1/2 + 5/18) = 0
-10x/3 +2y/3 + 7/9 = 0
-30x + 6y + 7 = 0
30x - 6y = 7
Without determinants:
Find the slope (m) of the line thru the 2 points
m = (y2-y1)/(x2-x1)
m = (3 + 1/3)/(5/6 - 1/6)
m = (10/3)/(2/3)
m = 5 (the slope of the line)
Then use point #2 (either will work, but #1 has 2 fractions)
y - y2 = m*(x - x2)
y - 3 = 5*(x - 5/6)
y - 3 = 5x - 25/6
6y - 18 = 30x - 25
30x - 6y = 7 Same answer, more work.

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