SOLUTION: Find the equation of the line through (-1,-7) having a slope of -6.

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Question 134197: Find the equation of the line through (-1,-7) having a slope of -6.
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(21685) 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 -6 which goes through the point (-1,-7), 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--7=%28-6%29%28x--1%29 Plug in m=-6, x%5B1%5D=-1, and y%5B1%5D=-7 (these values are given)


y%2B7=%28-6%29%28x--1%29 Rewrite y--7 as y%2B7


y%2B7=%28-6%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B7=-6x%2B%28-6%29%281%29 Distribute -6

y%2B7=-6x-6 Multiply -6 and 1 to get -6

y=-6x-6-7 Subtract 7 from both sides to isolate y

y=-6x-13 Combine like terms -6 and -7 to get -13
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Answer:


So the equation of the line with a slope of -6 which goes through the point (-1,-7) is:

y=-6x-13 which is now in y=mx%2Bb form where the slope is m=-6 and the y-intercept is b=-13

Notice if we graph the equation y=-6x-13 and plot the point (-1,-7), we get (note: if you need help with graphing, check out this solver)

drawing%28500%2C+500%2C+-10%2C+8%2C+-16%2C+2%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+8%2C+-16%2C+2%2C%28-6%29x%2B-13%29%2C%0D%0Acircle%28-1%2C-7%2C0.12%29%2C%0D%0Acircle%28-1%2C-7%2C0.12%2B0.03%29%0D%0A%29+ Graph of y=-6x-13 through the point (-1,-7)
and we can see that the point lies on the line. Since we know the equation has a slope of -6 and goes through the point (-1,-7), this verifies our answer.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=mX+b
-7=-6*-1+b
-7=6+b
b=-7-6
b=-13 THUS THE EQUATION IS:
Y=-6X-13
+graph%28+300%2C+200%2C+-6%2C+5%2C+-15%2C+10%2C+-6x+-13%29+ (graph 300x200 pixels, x from -6 to 5, y from -15 to 10, -6x -13).