SOLUTION: Find an equation of the line through points (-2,-4) and (-4,-3)

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Question 754649: Find an equation of the line through points (-2,-4) and (-4,-3)
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=-2 and y%5B1%5D=-4.
Also, is the second point . So this means that x%5B2%5D=-4 and y%5B2%5D=-3.


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


m=%28-3--4%29%2F%28-4--2%29 Plug in y%5B2%5D=-3, y%5B1%5D=-4, x%5B2%5D=-4, and x%5B1%5D=-2


m=%281%29%2F%28-4--2%29 Subtract -4 from -3 to get 1


m=%281%29%2F%28-2%29 Subtract -2 from -4 to get -2


m=-1%2F2 Reduce


So the slope of the line that goes through the points and is m=-1%2F2


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--4=%28-1%2F2%29%28x--2%29 Plug in m=-1%2F2, x%5B1%5D=-2, and y%5B1%5D=-4


y--4=%28-1%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B4=%28-1%2F2%29%28x%2B2%29 Rewrite y--4 as y%2B4


y%2B4=%28-1%2F2%29x%2B%28-1%2F2%29%282%29 Distribute


y%2B4=%28-1%2F2%29x-1 Multiply


y=%28-1%2F2%29x-1-4 Subtract 4 from both sides.


y=%28-1%2F2%29x-5 Combine like terms.


So the equation that goes through the points and is y=%28-1%2F2%29x-5