SOLUTION: What is the equation of the line that passes through the points (-8,-1) and (-2,23)?

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Question 530138: What is the equation of the line that passes through the points (-8,-1) and (-2,23)?
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=-8 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=23.


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


m=%2823--1%29%2F%28-2--8%29 Plug in y%5B2%5D=23, y%5B1%5D=-1, x%5B2%5D=-2, and x%5B1%5D=-8


m=%2824%29%2F%28-2--8%29 Subtract -1 from 23 to get 24


m=%2824%29%2F%286%29 Subtract -8 from -2 to get 6


m=4 Reduce


So the slope of the line that goes through the points and is m=4


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--1=4%28x--8%29 Plug in m=4, x%5B1%5D=-8, and y%5B1%5D=-1


y--1=4%28x%2B8%29 Rewrite x--8 as x%2B8


y%2B1=4%28x%2B8%29 Rewrite y--1 as y%2B1


y%2B1=4x%2B4%288%29 Distribute


y%2B1=4x%2B32 Multiply


y=4x%2B32-1 Subtract 1 from both sides.


y=4x%2B31 Combine like terms.


So the equation that goes through the points and is y=4x%2B31


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