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Question 1149757: A line has an x-intercept of 3 and a y-intercept of k and passes through a point (5,8). Find k.
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I encourage students to practice being able to solve a problem like this using your UNDERSTANDING of the problem, without the formal algebra. Being able to do that means you really understand the problem.
The given x-intercept is (3,0); the given point is (5,8).
The given point is 2 to the right and 8 above the x-intercept; the slope is 8/2 = 4.
The y-intercept is where x=0; that is 3 units to the left of the x-intercept.
With a slope of 4, 3 units to the left means 12 units down.
12 units down from the x-intercept gives a y value of -12.
Therefore the y-intercept is (0,-12).
ANSWER: k = -12
Answer by ikleyn(52797)  (Show Source):
You can put this solution on YOUR website! .
They want you find k in this way that the three points, P1= (3,0), P2= (0,k) and P3= (5,8) lie in one line.
It means that the slope from P1 to P2,  =  = 
should be equal to the slope from P2 to P3,  =  =  .
It gives you an equation
=
Cross multiply and solve for k
-5k = 3*(8-k)
-5k = 24 - 3k
-5k + 3k = 24
-2k = 24
k =  = -12. 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 presented solutions is 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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