SOLUTION: Write the equation of the line going through points (-3,2) and (2,-8)

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Question 913051: Write the equation of the line going through points (-3,2) and (2,-8)
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=2.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=-8.


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


m=%28-8-2%29%2F%282--3%29 Plug in y%5B2%5D=-8, y%5B1%5D=2, x%5B2%5D=2, and x%5B1%5D=-3


m=%28-10%29%2F%282--3%29 Subtract 2 from -8 to get -10


m=%28-10%29%2F%285%29 Subtract -3 from 2 to get 5


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


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


y-2=-2x%2B-2%283%29 Distribute


y-2=-2x-6 Multiply


y=-2x-6%2B2 Add 2 to both sides.


y=-2x-4 Combine like terms.


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


Notice how the graph of y=-2x-4 goes through the points and . So this visually verifies our answer.
Graph of y=-2x-4 through the points and

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim