SOLUTION: Please help. I need to find the equation of the line through (-3,1) with a slope of -1/3. thank you so much.

Algebra ->  Linear-equations -> SOLUTION: Please help. I need to find the equation of the line through (-3,1) with a slope of -1/3. thank you so much.      Log On


   

Question 194039: Please help. I need to find the equation of the line through (-3,1) with a slope of -1/3.
thank you so much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -1%2F3 which goes through the point (-3,1), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-1=%28-1%2F3%29%28x--3%29 Plug in m=-1%2F3, x%5B1%5D=-3, and y%5B1%5D=1 (these values are given)


y-1=%28-1%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-1=%28-1%2F3%29x%2B%28-1%2F3%29%283%29 Distribute -1%2F3


y-1=%28-1%2F3%29x-1 Multiply -1%2F3 and 3 to get -1


y=%28-1%2F3%29x-1%2B1 Add 1 to both sides to isolate y


y=%28-1%2F3%29x%2B0 Combine like terms -1 and 1 to get 0


y=-%281%2F3%29x Simplify
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Answer:


So the equation of the line with a slope of -1%2F3 which goes through the point (-3,1) is:


y=%28-1%2F3%29x%2B0 which is now in y=mx%2Bb form where the slope is m=-1%2F3 and the y-intercept is b=0


Notice if we graph the equation y=%28-1%2F3%29x%2B0 and plot the point (-3,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x through the point (-3,1)
and we can see that the point lies on the line. Since we know the equation has a slope of -1%2F3 and goes through the point (-3,1), this verifies our answer.