SOLUTION: what is the equation of the line that passes through points (-4,2) and (4,0)?

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Question 593817: what is the equation of the line that passes through points (-4,2) and (4,0)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=-4 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=0.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%280-2%29%2F%284--4%29 Plug in y%5B2%5D=0, y%5B1%5D=2, x%5B2%5D=4, and x%5B1%5D=-4


m=%28-2%29%2F%284--4%29 Subtract 2 from 0 to get -2


m=%28-2%29%2F%288%29 Subtract -4 from 4 to get 8


m=-1%2F4 Reduce


So the slope of the line that goes through the points and is m=-1%2F4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-2=%28-1%2F4%29%28x--4%29 Plug in m=-1%2F4, x%5B1%5D=-4, and y%5B1%5D=2


y-2=%28-1%2F4%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-2=%28-1%2F4%29x%2B%28-1%2F4%29%284%29 Distribute


y-2=%28-1%2F4%29x-1 Multiply


y=%28-1%2F4%29x-1%2B2 Add 2 to both sides.


y=%28-1%2F4%29x%2B1 Combine like terms.


So the equation that goes through the points and is y=%28-1%2F4%29x%2B1


Notice how the graph of y=%28-1%2F4%29x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=%28-1%2F4%29x%2B1 through the points and

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