SOLUTION: find an equation of the line that contains the following pair of points (4,1) (1,3)

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Question 567773: find an equation of the line that contains the following pair of points (4,1) (1,3)
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=4 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=1 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=%283-1%29%2F%281-4%29 Plug in y%5B2%5D=3, y%5B1%5D=1, x%5B2%5D=1, and x%5B1%5D=4


m=%282%29%2F%281-4%29 Subtract 1 from 3 to get 2


m=%282%29%2F%28-3%29 Subtract 4 from 1 to get -3


m=-2%2F3 Reduce


So the slope of the line that goes through the points and is m=-2%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-1=%28-2%2F3%29%28x-4%29 Plug in m=-2%2F3, x%5B1%5D=4, and y%5B1%5D=1


y-1=%28-2%2F3%29x%2B%28-2%2F3%29%28-4%29 Distribute


y-1=%28-2%2F3%29x%2B8%2F3 Multiply


y=%28-2%2F3%29x%2B8%2F3%2B1 Add 1 to both sides.


y=%28-2%2F3%29x%2B11%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=%28-2%2F3%29x%2B11%2F3