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

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Question 318423: Find an equation of the line containing the given pair of points (1/6, -1/3) and (5/6, 5)
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%2F6 and y%5B1%5D=-1%2F3.
Also, is the second point . So this means that x%5B2%5D=5%2F6 and y%5B2%5D=5.


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


m=%285--1%2F3%29%2F%285%2F6-1%2F6%29 Plug in y%5B2%5D=5, y%5B1%5D=-1%2F3, x%5B2%5D=5%2F6, and x%5B1%5D=1%2F6


m=%2816%2F3%29%2F%285%2F6-1%2F6%29 Subtract -1%2F3 from 5 to get 16%2F3


m=%2816%2F3%29%2F%282%2F3%29 Subtract 1%2F6 from 5%2F6 to get 2%2F3


m=%2816%2F3%29%2A%283%2F2%29 Multiply the first fraction by the reciprocal of the second fraction.


m=8 Multiply and reduce.


So the slope of the line that goes through the points and is m=8


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%2F3=8%28x-1%2F6%29 Plug in m=8, x%5B1%5D=1%2F6, and y%5B1%5D=-1%2F3


y%2B1%2F3=8%28x-1%2F6%29 Rewrite y--1%2F3 as y%2B1%2F3


y%2B1%2F3=8x%2B8%28-1%2F6%29 Distribute


y%2B1%2F3=8x-4%2F3 Multiply


y=8x-4%2F3-1%2F3 Subtract 1%2F3 from both sides.


y=8x-5%2F3 Combine like terms.


So the equation that goes through the points and is y=8x-5%2F3