SOLUTION: I had a line that goes through (12,-9) and has a slope of -1/3 would it be y=-1/3x+5

Algebra ->  Graphs -> SOLUTION: I had a line that goes through (12,-9) and has a slope of -1/3 would it be y=-1/3x+5      Log On


   

Question 149473: I had a line that goes through (12,-9) and has a slope of -1/3 would it be y=-1/3x+5
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 (12,-9), 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--9=%28-1%2F3%29%28x-12%29 Plug in m=-1%2F3, x%5B1%5D=12, and y%5B1%5D=-9 (these values are given)


y%2B9=%28-1%2F3%29%28x-12%29 Rewrite y--9 as y%2B9


y%2B9=%28-1%2F3%29x%2B%28-1%2F3%29%28-12%29 Distribute -1%2F3

y%2B9=%28-1%2F3%29x%2B4 Multiply -1%2F3 and -12 to get 4

y=%28-1%2F3%29x%2B4-9 Subtract 9 from both sides to isolate y

y=%28-1%2F3%29x-5 Combine like terms 4 and -9 to get -5
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line with a slope of -1%2F3 which goes through the point (12,-9) is:

y=%28-1%2F3%29x-5 which is now in y=mx%2Bb form where the slope is m=-1%2F3 and the y-intercept is b=-5

Notice if we graph the equation y=%28-1%2F3%29x-5 and plot the point (12,-9), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x-5 through the point (12,-9)
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 (12,-9), this verifies our answer.