SOLUTION: what is the equation, slope, and y-intercept of (-1,6) and (1,7)?

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Question 555818: what is the equation, slope, and y-intercept of (-1,6) and (1,7)?
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=-1 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=1 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=%287-6%29%2F%281--1%29 Plug in y%5B2%5D=7, y%5B1%5D=6, x%5B2%5D=1, and x%5B1%5D=-1


m=%281%29%2F%281--1%29 Subtract 6 from 7 to get 1


m=%281%29%2F%282%29 Subtract -1 from 1 to get 2


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-6=%281%2F2%29%28x--1%29 Plug in m=1%2F2, x%5B1%5D=-1, and y%5B1%5D=6


y-6=%281%2F2%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-6=%281%2F2%29x%2B%281%2F2%29%281%29 Distribute


y-6=%281%2F2%29x%2B1%2F2 Multiply


y=%281%2F2%29x%2B1%2F2%2B6 Add 6 to both sides.


y=%281%2F2%29x%2B13%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%281%2F2%29x%2B13%2F2

The equation is y = mx+b form where m is the slope and (0, b) is the y intercept


So because m = 1/2, we see that the slope is 1/2


Since b = 13/2, the y-intercept is (0, 13/2)

If you need more help, email me at jim_thompson5910@hotmail.com

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Jim