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Question 1149758: Find the value of k that makes the line through (-4, k) and (-1,2k) have a y-intercept of -7.
Found 4 solutions by josmiceli, MathLover1, greenestamps, ikleyn:
Answer by josmiceli(19441)   (Show Source):
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! if the line through (-4, k) and (-1,2k) you can find a slope
slope is:
y-intercept of  : ( , )
if the line have a y-intercept of , use slope intercept formula
 where  is y-intercept and  is a slope, substitute both
 .......use point, ( ,  )
 ....solve for 
 ...both sides multiply by 
then slope is  => =>
so, the line is:
 ,
and two points will be:
( ,  ) and (, )
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I encourage students to practice being able to solve problems like this using your UNDERSTANDING of the problem, without the formal algebra.
As you will see (comparing my solution method with those shown in the other responses you have gotten), finding the answer is much easier this way (if you understand it!) than with the formal algebra.
(1) The line passes through the points (-4,k) and (-1,2k). So in moving 3 to the right, from -4 to -1, the y value changes by k, from k to 2k.
(2) We want the value of k that makes the y-intercept -7.
(3) The y-intercept is when x=0, which is 1 unit to the right of (-1,2k).
(4) Since this is a straight line, changing the y value by k when the x value changes by 3 means changing the y value by k/3 when the value of x changes by 1.
(5) So the y-intercept is at (0,2k+k/3), or (0,7k/3).
(6) Since we want the y-intercept to be (0,-7),
ANSWER: k = -3
Answer by ikleyn(52795)  (Show Source):
You can put this solution on YOUR website! .
They want you find k in this way that the three points, P1= (-4,k), P2= (-1,2k) and P3= (0,-7) lie in one line.
It means that the slope from P1 to P2,  =  = 
should be equal to the slope from P2 to P3,  =  =  = -7-2k.
It gives you an equation
= -7 - 2k
k = -21 - 6k
k + 6k = - 21
7k = - 21
k =  = -3. ANSWER
Solved.
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It is pure Algebra solution (Algebra to which we teach at this site), presented in a way as it SHOULD BE presented,
and now you can compare which of the 4 solutions is simpler and better for you.
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Regarding incantations from @greenestamps, keep in mind that they are very subjective and reflect his personal opinion.
Other people may have DIFFERENT, or VERY DIFFERENT, or even OPPOSITE opinion.
Personal opinion weights nothing as an argument when you evaluate methods.
If you want to see Algebra method and solution (and I think that you came to this forum exactly for it), you have them
here before your eyes.
And if you want to learn them, you may learn them from this source.
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