SOLUTION: Find an equation of the line containing the given pair of points. (-5,-9) and (-2,-8)

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Question 640632: Find an equation of the line containing the given pair of points.
(-5,-9) and (-2,-8)
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=-5 and y%5B1%5D=-9.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=-8.


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


m=%28-8--9%29%2F%28-2--5%29 Plug in y%5B2%5D=-8, y%5B1%5D=-9, x%5B2%5D=-2, and x%5B1%5D=-5


m=%281%29%2F%28-2--5%29 Subtract -9 from -8 to get 1


m=%281%29%2F%283%29 Subtract -5 from -2 to get 3


So the slope of the line that goes through the points and is m=1%2F3


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--9=%281%2F3%29%28x--5%29 Plug in m=1%2F3, x%5B1%5D=-5, and y%5B1%5D=-9


y--9=%281%2F3%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B9=%281%2F3%29%28x%2B5%29 Rewrite y--9 as y%2B9


y%2B9=%281%2F3%29x%2B%281%2F3%29%285%29 Distribute


y%2B9=%281%2F3%29x%2B5%2F3 Multiply


y=%281%2F3%29x%2B5%2F3-9 Subtract 9 from both sides.


y=%281%2F3%29x-22%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%281%2F3%29x-22%2F3