SOLUTION: Find the equation of the line through the points (-3,-1) and (-9,-6)

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Question 274739: Find the equation of the line through the points (-3,-1) and (-9,-6)
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=-1.
Also, is the second point . So this means that x%5B2%5D=-9 and y%5B2%5D=-6.


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


m=%28-6--1%29%2F%28-9--3%29 Plug in y%5B2%5D=-6, y%5B1%5D=-1, x%5B2%5D=-9, and x%5B1%5D=-3


m=%28-5%29%2F%28-9--3%29 Subtract -1 from -6 to get -5


m=%28-5%29%2F%28-6%29 Subtract -3 from -9 to get -6


m=5%2F6 Reduce


So the slope of the line that goes through the points and is m=5%2F6

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Now remember that the general slope intercept equation is y=mx%2Bb where 'm' is the slope of the line and 'b' is the y-intercept. We can use this general equation to find the equation of the line.

Since the line goes through the point (-3,-1), this means that x=-3 and y=-1. In addition, we know that the slope is m=5%2F6. So we can use these values to solve for 'b'.


y=mx%2Bb Start with the general slope-intercept equation.


-1=%285%2F6%29%28-3%29%2Bb Plug in x=-3, y=-1 and m=5%2F6


-1=-15%2F6%2Bb Multiply.


-1=-5%2F2%2Bb Reduce.


-1%2B5%2F2=b Add 5%2F2 to both sides to isolate 'b'


3%2F2=b Combine like terms.


So the value of 'b' is b=3%2F2


Since m=5%2F6 and b=3%2F2, we can plug these values into y=mx%2Bb to get y=%285%2F6%29x%2B3%2F2


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Answer:

So the equation of the line in slope-intercept form through the points (-3,-1) and (-9,-6) is y=%285%2F6%29x%2B3%2F2