SOLUTION: find the equation of the line containing the given pair of points. (-3,-6) and (-7,-1)

Algebra ->  Linear-equations -> SOLUTION: find the equation of the line containing the given pair of points. (-3,-6) and (-7,-1)      Log On


   

Question 514808: find the equation of the line containing the given pair of points. (-3,-6) and (-7,-1)
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=-6.
Also, is the second point . So this means that x%5B2%5D=-7 and y%5B2%5D=-1.


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


m=%28-1--6%29%2F%28-7--3%29 Plug in y%5B2%5D=-1, y%5B1%5D=-6, x%5B2%5D=-7, and x%5B1%5D=-3


m=%285%29%2F%28-7--3%29 Subtract -6 from -1 to get 5


m=%285%29%2F%28-4%29 Subtract -3 from -7 to get -4


m=-5%2F4 Reduce


So the slope of the line that goes through the points and is m=-5%2F4


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=%28-5%2F4%29%28x--3%29 Plug in m=-5%2F4, x%5B1%5D=-3, and y%5B1%5D=-6


y--6=%28-5%2F4%29%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B6=%28-5%2F4%29%28x%2B3%29 Rewrite y--6 as y%2B6


y%2B6=%28-5%2F4%29x%2B%28-5%2F4%29%283%29 Distribute


y%2B6=%28-5%2F4%29x-15%2F4 Multiply


y=%28-5%2F4%29x-15%2F4-6 Subtract 6 from both sides.


y=%28-5%2F4%29x-39%2F4 Combine like terms.