SOLUTION: Find an equation of the line containing the given pair of points. (-3,-8) and (-9,-5) The equation of the line in slope-intercept form is y=

Algebra ->  Systems-of-equations -> SOLUTION: Find an equation of the line containing the given pair of points. (-3,-8) and (-9,-5) The equation of the line in slope-intercept form is y=      Log On


   

Question 583793: Find an equation of the line containing the given pair of points.
(-3,-8) and (-9,-5)
The equation of the line in slope-intercept form is y=
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=-8.
Also, is the second point . So this means that x%5B2%5D=-9 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=%28-5--8%29%2F%28-9--3%29 Plug in y%5B2%5D=-5, y%5B1%5D=-8, x%5B2%5D=-9, and x%5B1%5D=-3


m=%283%29%2F%28-9--3%29 Subtract -8 from -5 to get 3


m=%283%29%2F%28-6%29 Subtract -3 from -9 to get -6


m=-1%2F2 Reduce


So the slope of the line that goes through the points and is m=-1%2F2


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--8=%28-1%2F2%29%28x--3%29 Plug in m=-1%2F2, x%5B1%5D=-3, and y%5B1%5D=-8


y--8=%28-1%2F2%29%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B8=%28-1%2F2%29%28x%2B3%29 Rewrite y--8 as y%2B8


y%2B8=%28-1%2F2%29x%2B%28-1%2F2%29%283%29 Distribute


y%2B8=%28-1%2F2%29x-3%2F2 Multiply


y=%28-1%2F2%29x-3%2F2-8 Subtract 8 from both sides.


y=%28-1%2F2%29x-19%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-1%2F2%29x-19%2F2

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Jim