SOLUTION: Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear.

Question 1010002: Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear.
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Look at the slopes::
1st point to 3rd point::
(k-4)/(0+3) = (10-4)/(k+3)
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Cross multiply::
k^2 - k - 12 = 3*6
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k^2 - k - 30 = 0
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(k-6)(k+5) = 0
k = 6 or k = -5
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Cheers,
Stan H.
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Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Find two values of k such that the points (,), (,), and (,) are collinear.
the points are collinear if they lie on same line
use the slope of a line to find

for the points (,), (,),

.............eq.1
for (,), and (,)

............eq.2
from eq.1 and eq.2 we have
............cross multiply

...........factor completely

solutions:

so, the points (,), (,), and (,) are collinear
and the points (,), (,), and (,) are collinear
now find slope
.............eq.1 if

.............eq.1 if

so, there are possible lines and they are
and

we need y-intercepts
use one point : (,)

and
use one point : (,)

so, the line contains points the points (,), (,), and (,)

and the line contains points the points (,), (,), and (,)

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