SOLUTION: what is the equation for (-3,12) and (0,10) along with the slope and y-intercept?

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Question 555808: what is the equation for (-3,12) and (0,10) along with the slope and y-intercept?
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=12.
Also, is the second point . So this means that x%5B2%5D=0 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=%2810-12%29%2F%280--3%29 Plug in y%5B2%5D=10, y%5B1%5D=12, x%5B2%5D=0, and x%5B1%5D=-3


m=%28-2%29%2F%280--3%29 Subtract 12 from 10 to get -2


m=%28-2%29%2F%283%29 Subtract -3 from 0 to get 3


So the slope of the line that goes through the points and is m=-2%2F3


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-12=%28-2%2F3%29%28x--3%29 Plug in m=-2%2F3, x%5B1%5D=-3, and y%5B1%5D=12


y-12=%28-2%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-12=%28-2%2F3%29x%2B%28-2%2F3%29%283%29 Distribute


y-12=%28-2%2F3%29x-2 Multiply


y=%28-2%2F3%29x-2%2B12 Add 12 to both sides.


y=%28-2%2F3%29x%2B10 Combine like terms.


So the equation that goes through the points and is y=%28-2%2F3%29x%2B10


The equation is now in y = mx+b form where m=-2%2F3 and b=10


So the slope is -2%2F3 and the y-intercept is (0,10)

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Jim