SOLUTION: Write the equation of the line passing through (4, –4) and (2, 0).

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Question 102633: Write the equation of the line passing through (4, –4) and (2, 0).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (4,-4) and (2,0)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (4,-4) and is the second point (2,0))

m=%280--4%29%2F%282-4%29 Plug in y%5B2%5D=0,y%5B1%5D=-4,x%5B2%5D=2,x%5B1%5D=4 (these are the coordinates of given points)

m=+4%2F-2 Subtract the terms in the numerator 0--4 to get 4. Subtract the terms in the denominator 2-4 to get -2


m=-2 Reduce

So the slope is
m=-2

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y--4=%28-2%29%28x-4%29 Plug in m=-2, x%5B1%5D=4, and y%5B1%5D=-4 (these values are given)


y%2B4=%28-2%29%28x-4%29 Rewrite y--4 as y%2B4


y%2B4=-2x%2B%28-2%29%28-4%29 Distribute -2

y%2B4=-2x%2B8 Multiply -2 and -4 to get 8

y=-2x%2B8-4 Subtract 4 from both sides to isolate y

y=-2x%2B4 Combine like terms 8 and -4 to get 4
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Answer:


So the equation of the line which goes through the points (4,-4) and (2,0) is:y=-2x%2B4

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2 and the y-intercept is b=4

Notice if we graph the equation y=-2x%2B4 and plot the points (4,-4) and (2,0), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-2x%2B4 through the points (4,-4) and (2,0)

Notice how the two points lie on the line. This graphically verifies our answer.