SOLUTION: Find the equation of the line passing through the points (3,8) and (2,5)

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Question 605330: Find the equation of the line passing through the points (3,8) and (2,5)
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=3 and y%5B1%5D=8.
Also, is the second point . So this means that x%5B2%5D=2 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=%285-8%29%2F%282-3%29 Plug in y%5B2%5D=5, y%5B1%5D=8, x%5B2%5D=2, and x%5B1%5D=3


m=%28-3%29%2F%282-3%29 Subtract 8 from 5 to get -3


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


m=3 Reduce


So the slope of the line that goes through the points and is m=3


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-8=3%28x-3%29 Plug in m=3, x%5B1%5D=3, and y%5B1%5D=8


y-8=3x%2B3%28-3%29 Distribute


y-8=3x-9 Multiply


y=3x-9%2B8 Add 8 to both sides.


y=3x-1 Combine like terms.


So the equation that goes through the points and is y=3x-1


Notice how the graph of y=3x-1 goes through the points and . So this visually verifies our answer.
Graph of y=3x-1 through the points and



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