SOLUTION: Find an equation of the line that satisfies the given conditions. Through (−1, −2) and (6, 5)

Algebra ->  Equations -> SOLUTION: Find an equation of the line that satisfies the given conditions. Through (−1, −2) and (6, 5)       Log On


   

Question 527243: Find an equation of the line that satisfies the given conditions.
Through
(−1, −2) and (6, 5)
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=-2.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=5.


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


m=%285--2%29%2F%286--1%29 Plug in y%5B2%5D=5, y%5B1%5D=-2, x%5B2%5D=6, and x%5B1%5D=-1


m=%287%29%2F%286--1%29 Subtract -2 from 5 to get 7


m=%287%29%2F%287%29 Subtract -1 from 6 to get 7


m=1 Reduce


So the slope of the line that goes through the points and is m=1


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


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


y%2B2=1%28x%2B1%29 Rewrite y--2 as y%2B2


y%2B2=1x%2B1%281%29 Distribute


y%2B2=1x%2B1 Multiply


y=1x%2B1-2 Subtract 2 from both sides.


y=1x-1 Combine like terms.


y=x-1 Simplify


So the equation that goes through the points and is y=x-1


Notice how the graph of y=x-1 goes through the points and . So this visually verifies our answer.
Graph of y=x-1 through the points and



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