SOLUTION: Derive the equation of the line that passes through point (4, -16) with a slope of -3.

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Question 110755: Derive the equation of the line that passes through point (4, -16) with a slope of -3.
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the point-slope form allows you to write the equation directly

y-(-16)=(-3)(x-(4))

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 -3 which goes through the point (4,-16), 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--16=%28-3%29%28x-4%29 Plug in m=-3, x%5B1%5D=4, and y%5B1%5D=-16 (these values are given)


y%2B16=%28-3%29%28x-4%29 Rewrite y--16 as y%2B16


y%2B16=-3x%2B%28-3%29%28-4%29 Distribute -3

y%2B16=-3x%2B12 Multiply -3 and -4 to get 12

y=-3x%2B12-16 Subtract 16 from both sides to isolate y

y=-3x-4 Combine like terms 12 and -16 to get -4
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Answer:


So the equation of the line with a slope of -3 which goes through the point (4,-16) is:

y=-3x-4 which is now in y=mx%2Bb form where the slope is m=-3 and the y-intercept is b=-4

Notice if we graph the equation y=-3x-4 and plot the point (4,-16), we get (note: if you need help with graphing, check out this solver)

Graph of y=-3x-4 through the point (4,-16)
and we can see that the point lies on the line. Since we know the equation has a slope of -3 and goes through the point (4,-16), this verifies our answer.