SOLUTION: write the equation of the line that passes through point (-1,11) with a slope of -5

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Question 87777: write the equation of the line that passes through point (-1,11) with a slope of -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 -5 which goes through the point (-1,11), 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 (x%5B1%5D,y%5B1%5D) is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-11=%28-5%29%28x--1%29 Plug in m=-5, x%5B1%5D=-1, and y%5B1%5D=11 (these values are given)

y-11=%28-5%29x-%28-5%29%28-1%29%29 Distribute -5

y-11=%28-5%29x%2B%285%29%28-1%29%29 Multiply the negatives

y-11=%28-5%29x%2B-5 Multiply 5 and -1 to get -5

y=%28-5%29x%2B-5%2B11Add 11 to both sides

y=%28-5%29x%2B6 Combine like terms
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Answer:


So the equation of the line with a slope of -5 which goes through the point (-1,11) is:

y=%28-5%29x%2B6 which is now in y=mx%2Bb form where the slope is m=-5 (so this shows our equation has a slope of -5) and the y-intercept is b=6

Notice if we graph the equation y=%28-5%29x%2B6 (note: if you need help with graphing, check out this solver) and plot the point (-1,11), we get

Graph of y=%28-5%29x%2B6 through the point (-1,11)
and we can see that the point lies on the line. Since we know the equation has a slope of -5 and goes through the point (-1,11), this verifies our answer.