Question 283485: find the equation of the line that passes through (4,-3) and (8,-5)
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We are seeking an equation for a line that will go through the points (4,-3) and (8,-5).
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We know the slope-intercept form of the equation is: y = mx+b
m = slope
b = y-intercept
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m = rise / run = change in y / change in x
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m = (y2-y1)/(x2-x1)
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(4,-3) = (x1,y1)
(8,-5) = (x2,y2)
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m = (-5 -(-3)) / (8 -4) = (-5 +3) / (8 -4) = -2/4 = -1/2
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y = -1/2x + b
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Now we can substitute what we know to find 'b'.
For example, one of the points is (4,-3).
Substituting for x and y...
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-3 = -1/2(4) + b
-3 = -2 + b
-1 = b
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And we know the other point is (8,-5)
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-5 = -1/2(8) + b
-5 = -4 + b
-1 = b
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b = -1 = y-intercept = (0,-1)
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y = -1/2x -1
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Another useful point to find is the x-intercept, which is where y=0.
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0 = -1/2x -1
1/2x = -1
x = -2
(-2,0)
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Graph to check
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Answer:
The equation is
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Done
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