SOLUTION: write an equation of the line passing through the given points (1,-14) and (-2,7)

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Question 172181: write an equation of the line passing through the given points
(1,-14) and (-2,7)
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


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


m=%287--14%29%2F%28-2-1%29 Plug in y%5B2%5D=7, y%5B1%5D=-14, x%5B2%5D=-2, and x%5B1%5D=1


m=%2821%29%2F%28-2-1%29 Subtract -14 from 7 to get 21


m=%2821%29%2F%28-3%29 Subtract 1 from -2 to get -3


m=-7 Reduce


So the slope of the line that goes through the points and is m=-7


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--14=-7%28x-1%29 Plug in m=-7, x%5B1%5D=1, and y%5B1%5D=-14


y%2B14=-7%28x-1%29 Rewrite y--14 as y%2B14


y%2B14=-7x%2B-7%28-1%29 Distribute


y%2B14=-7x%2B7 Multiply


y=-7x%2B7-14 Subtract 14 from both sides.


y=-7x-7 Combine like terms.



So the equation that goes through the points and is y=-7x-7


Notice how the graph of y=-7x-7 goes through the points and . So this visually verifies our answer.
Graph of y=-7x-7 through the points and