SOLUTION: Use an equation to find the value of k so that the line that passes through the given points has the given slope. (−4,k), (6,−7); m=−one/fifth

Algebra ->  Linear-equations -> SOLUTION: Use an equation to find the value of k so that the line that passes through the given points has the given slope. (−4,k), (6,−7); m=−one/fifth       Log On


   

Question 1154205: Use an equation to find the value of k so that the line that passes through the given points has the given slope.
(−4,k), (6,−7); m=−one/fifth

Found 3 solutions by josgarithmetic, mananth, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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(−4,k), (6,−7); m=−one/fifth
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?
Is that, m=-1%2F5?

%28k-%28-7%29%29%2F%28-4-6%29=-1%2F5
Simplification:
-%28k%2B7%29%2F10=-1%2F5
%28k%2B7%29%2F10=1%2F5
k%2B7=2
highlight%28k=-5%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The general equation of a line when two points are given
%28y1-y2%29%2F%28x1-x2%29+=+m
plug the values
%28k-%28-7%29%29%2F+%28-4-6%29+=+-%281%2F5%29

%28k%2B7%29%2F-10+=+-1%2F5+
5k+35=10
5k=-25
k=-5

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I prefer to use my understanding of slope, rather than a mathematical formula, to solve problems like this.

I also encourage students to do that, since it helps gain an understanding of slope, whereas plugging numbers into a formula does not.

(Furthermore, if you plug the numbers in the wrong places in the formula, you probably won't get the right answer....)

The second of the two given points is 10 to the right of the first.
Since the slope is -1/5, the second point must be 2 down from the first.
2 down from the first, ending at -7, means the y coordinate of the first point is -5.

ANSWER: k = -5