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Points (-5, -7) and (3, -4) lie on the same line

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by jsl » Mon Oct 27, 2008 3:16 pm
Points (-5, -7) and (3, -4) lie on the same line in an X-Y plane. If point (x, 8) also lies on the same line, what is x??

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Last edited by jsl on Tue Oct 28, 2008 4:26 am, edited 1 time in total.
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by Ian Stewart » Mon Oct 27, 2008 3:26 pm
I think you mean (x, 8) lies on the line (disable smilies! :) ). If you can find the equation of the line, you can plug in y=8, solve for x, and you're done. We can find the equation of the line in two ways:

find the slope, using (y_2 - y_1)/(x_2 - x_1), then plug in a point to find the y-intercept.

or, plug both points into the equation y=mx + b, and solve for m and b (this is normally fastest, so that's what I'll do):

-7 = -5m + b
- -4 = 3m + b
-3 = -8m
m = 3/8
b = -41/8

So y = (3/8)x - 41/8

Plug in y=8:

8 = (3/8)x - 41/8
64 = 3x - 41
105 = 3x
35 = x
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by rohangupta83 » Mon Oct 27, 2008 3:48 pm
or we could just find the slope and use it:

m = [-4 - (-7)]/[3 - (-5)]

m = (-4+7)/(3+5)
m = 3/8

which should also be the slow for points (x,8) and (3,-4) as they all lay on the same line.

3/8 = (-4 -8)/(3-x)
3/8 = -12/(3-x)
3(3-x) = -12*8
9-3x = -96
9+96 = 3x
105 = 3x
x=105/3
x=35
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