SOLUTION: A line passes through the points (k=3,-2k) and (4,1) and has a y-intercept of 6. Find the value of k.

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Question 363036: A line passes through the points (k=3,-2k) and (4,1) and has a y-intercept of 6. Find the value of k.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the question is:
A line passes through the points (k+3,-2k) and (4,1) and has a y-intercept of 6.
Find the value of k.
:
Assign the given points as follows
x1=(k+3); y1=-2k
x2=4; y2=1
:
Find the slope using these points: m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29
m = %28%281-%28-2k%29%29%29%2F%28%284-%28k%2B3%29%29%29 = %28%281%2B2k%29%29%2F%28%281-k%29%29 is the slope
:
Write the slope intercept form
y = %28%281%2B2k%29%29%2F%28%281-k%29%29x + 6
Substitute 4 for x and 1 for y; solve for k
%28%281%2B2k%29%29%2F%28%281-k%29%29(4) + 6 = 1
%284%281%2B2k%29%29%2F%28%281-k%29%29 = 1 - 6
%28%284%2B8k%29%29%2F%28%281-k%29%29 = -5
multiply both sides by (1-k), results
4 + 8k = -5(1-k)
4 + 8k = -5 + 5k
8k - 5k = -4 - 4
3k = -9
k + %28-9%29%2F3
k = -3
:
Check solution find the value of the 1st pair as given:
(k+3,-2k)
-3+3, -2(-3) = 0, 6