SOLUTION: Write the equation of the line that passes through (5,8) and (3,2) thank you

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Question 197569: Write the equation of the line that passes through (5,8) and (3,2)

thank you
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 and is the second point .


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


m=%282-8%29%2F%283-5%29 Plug in y%5B2%5D=2, y%5B1%5D=8, x%5B2%5D=3, and x%5B1%5D=5


m=%28-6%29%2F%283-5%29 Subtract 8 from 2 to get -6


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


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


y-8=3x%2B3%28-5%29 Distribute


y-8=3x-15 Multiply


y=3x-15%2B8 Add 8 to both sides.


y=3x-7 Combine like terms.


y=3x-7 Simplify


So the equation that goes through the points and is y=3x-7


Notice how the graph of y=3x-7 goes through the points and . So this visually verifies our answer.
Graph of y=3x-7 through the points and