SOLUTION: If the three points (a,b) , (3,0) and (4,8) are collinear, find the equations of a and b

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Question 1023464: If the three points (a,b) , (3,0) and (4,8) are collinear, find the equations of a and b
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
(a,b) must lie on the line through (3,0) and (4,8), which is
the line below.  The red points labeled (a,b) are several of 
the infinitely many possible points that (a,b) could be:



So we find the equation of that line using the
slope formula, and then the point-slope formula:

The slope formula is

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = (3,0)
and where (x2,y2) = (4,8)

m = %288-0%29%2F%284-3%29 = 8%2F1 = 8

The point-slope formula is

y - y1 = m(x - x1)
where (x1,y1) = (3,0)

y - 0 = 8(x - 3)
    y = 8x - 24

We can substitute x=a and y=b and get an equation

    b = 8a - 24

which is true for ANY point (a,b) on the above line,
[including the two given points!]

Edwin