SOLUTION: Please help to find an equation of the line that passes through (-3,6) and has a slope m = -2. Thank You

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Question 146190: Please help to find an equation of the line that passes through (-3,6) and has a slope m = -2.
Thank You
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 -2 which goes through the point (-3,6), 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-6=%28-2%29%28x--3%29 Plug in m=-2, x%5B1%5D=-3, and y%5B1%5D=6 (these values are given)


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


y-6=-2x%2B%28-2%29%283%29 Distribute -2

y-6=-2x-6 Multiply -2 and 3 to get -6

y=-2x-6%2B6 Add 6 to both sides to isolate y

y=-2x%2B0 Combine like terms -6 and 6 to get 0

y=-2x Remove the zero term

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Answer:


So the equation of the line with a slope of -2 which goes through the point (-3,6) is:


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

Notice if we graph the equation y=-2x and plot the point (-3,6), we get (note: if you need help with graphing, check out this solver)

Graph of y=-2x through the point (-3,6)
and we can see that the point lies on the line. Since we know the equation has a slope of -2 and goes through the point (-3,6), this verifies our answer.