SOLUTION: write the equation of a line passing through. (5,6)and (7,10)

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Question 713437: write the equation of a line passing through. (5,6)and (7,10)
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=5 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=10.


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


m=%2810-6%29%2F%287-5%29 Plug in y%5B2%5D=10, y%5B1%5D=6, x%5B2%5D=7, and x%5B1%5D=5


m=%284%29%2F%287-5%29 Subtract 6 from 10 to get 4


m=%284%29%2F%282%29 Subtract 5 from 7 to get 2


m=2 Reduce


So the slope of the line that goes through the points and is m=2


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-6=2%28x-5%29 Plug in m=2, x%5B1%5D=5, and y%5B1%5D=6


y-6=2x%2B2%28-5%29 Distribute


y-6=2x-10 Multiply


y=2x-10%2B6 Add 6 to both sides.


y=2x-4 Combine like terms.


So the equation that goes through the points and is y=2x-4