SOLUTION: What equation describes the line that contains the points (7,17) and 15,33)?

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Question 458667: What equation describes the line that contains the points (7,17) and 15,33)?
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=7 and y%5B1%5D=17.
Also, is the second point . So this means that x%5B2%5D=15 and y%5B2%5D=33.


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


m=%2833-17%29%2F%2815-7%29 Plug in y%5B2%5D=33, y%5B1%5D=17, x%5B2%5D=15, and x%5B1%5D=7


m=%2816%29%2F%2815-7%29 Subtract 17 from 33 to get 16


m=%2816%29%2F%288%29 Subtract 7 from 15 to get 8


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-17=2%28x-7%29 Plug in m=2, x%5B1%5D=7, and y%5B1%5D=17


y-17=2x%2B2%28-7%29 Distribute


y-17=2x-14 Multiply


y=2x-14%2B17 Add 17 to both sides.


y=2x%2B3 Combine like terms.


So the equation that goes through the points and is y=2x%2B3