SOLUTION: Find an equation of the line containing the given pair of points (-1,-3) and (-5,-6).

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Question 236559: Find an equation of the line containing the given pair of points (-1,-3) and (-5,-6).

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=-1 and y%5B1%5D=-3.
Also, is the second point . So this means that x%5B2%5D=-5 and y%5B2%5D=-6.


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


m=%28-6--3%29%2F%28-5--1%29 Plug in y%5B2%5D=-6, y%5B1%5D=-3, x%5B2%5D=-5, and x%5B1%5D=-1


m=%28-3%29%2F%28-5--1%29 Subtract -3 from -6 to get -3


m=%28-3%29%2F%28-4%29 Subtract -1 from -5 to get -4


m=3%2F4 Reduce


So the slope of the line that goes through the points and is m=3%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--3=%283%2F4%29%28x--1%29 Plug in m=3%2F4, x%5B1%5D=-1, and y%5B1%5D=-3


y--3=%283%2F4%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B3=%283%2F4%29%28x%2B1%29 Rewrite y--3 as y%2B3


y%2B3=%283%2F4%29x%2B%283%2F4%29%281%29 Distribute


y%2B3=%283%2F4%29x%2B3%2F4 Multiply


y=%283%2F4%29x%2B3%2F4-3 Subtract 3 from both sides.


y=%283%2F4%29x-9%2F4 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=%283%2F4%29x-9%2F4


Notice how the graph of y=%283%2F4%29x-9%2F4 goes through the points and . So this visually verifies our answer.
Graph of y=%283%2F4%29x-9%2F4 through the points and