SOLUTION: Write the equation of the line that passes through point (7, –18) with a slope of –2.

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Question 114186: Write the equation of the line that passes through point (7, –18) with a slope of –2.
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 (7,-18), 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--18=%28-2%29%28x-7%29 Plug in m=-2, x%5B1%5D=7, and y%5B1%5D=-18 (these values are given)


y%2B18=%28-2%29%28x-7%29 Rewrite y--18 as y%2B18


y%2B18=-2x%2B%28-2%29%28-7%29 Distribute -2

y%2B18=-2x%2B14 Multiply -2 and -7 to get 14

y=-2x%2B14-18 Subtract 18 from both sides to isolate y

y=-2x-4 Combine like terms 14 and -18 to get -4
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Answer:


So the equation of the line with a slope of -2 which goes through the point (7,-18) is:

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

Notice if we graph the equation y=-2x-4 and plot the point (7,-18), we get (note: if you need help with graphing, check out this solver)

Graph of y=-2x-4 through the point (7,-18)
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 (7,-18), this verifies our answer.