SOLUTION: Find an equation of the line containing the given pair of points (2,5) and (6,7)

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Question 567787: Find an equation of the line containing the given pair of points (2,5) and (6,7)
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=5.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=7.


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


m=%287-5%29%2F%286-2%29 Plug in y%5B2%5D=7, y%5B1%5D=5, x%5B2%5D=6, and x%5B1%5D=2


m=%282%29%2F%286-2%29 Subtract 5 from 7 to get 2


m=%282%29%2F%284%29 Subtract 2 from 6 to get 4


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-5=%281%2F2%29%28x-2%29 Plug in m=1%2F2, x%5B1%5D=2, and y%5B1%5D=5


y-5=%281%2F2%29x%2B%281%2F2%29%28-2%29 Distribute


y-5=%281%2F2%29x-1 Multiply


y=%281%2F2%29x-1%2B5 Add 5 to both sides.


y=%281%2F2%29x%2B4 Combine like terms.


y=%281%2F2%29x%2B4 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B4


Notice how the graph of y=%281%2F2%29x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B4 through the points and