SOLUTION: write an equation of a line that goes through the given points:(-2,-6)(-1,2)

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Question 307182: write an equation of a line that goes through the given points:(-2,-6)(-1,2)
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=-2 and y%5B1%5D=-6.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=2.


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


m=%282--6%29%2F%28-1--2%29 Plug in y%5B2%5D=2, y%5B1%5D=-6, x%5B2%5D=-1, and x%5B1%5D=-2


m=%288%29%2F%28-1--2%29 Subtract -6 from 2 to get 8


m=%288%29%2F%281%29 Subtract -2 from -1 to get 1


m=8 Reduce


So the slope of the line that goes through the points and is m=8


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=8%28x--2%29 Plug in m=8, x%5B1%5D=-2, and y%5B1%5D=-6


y--6=8%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B6=8%28x%2B2%29 Rewrite y--6 as y%2B6


y%2B6=8x%2B8%282%29 Distribute


y%2B6=8x%2B16 Multiply


y=8x%2B16-6 Subtract 6 from both sides.


y=8x%2B10 Combine like terms.


So the equation that goes through the points and is y=8x%2B10


Notice how the graph of y=8x%2B10 goes through the points and . So this visually verifies our answer.
Graph of y=8x%2B10 through the points and