SOLUTION: How can I Write the equation of the line that passes through point (2, –6) with a slope of –5.thank you in advance

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Question 90390: How can I Write the equation of the line that passes through point (2, –6) with a slope of –5.thank you in advance
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 (2,-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 (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--6=%28-5%29%28x-2%29 Plug in m=-5, x%5B1%5D=2, and y%5B1%5D=-6 (these values are given)

y--6=%28-5%29x-%28-5%29%282%29%29 Distribute -5

y--6=%28-5%29x%2B%285%29%282%29%29 Multiply the negatives

y%2B6=%28-5%29x%2B10 Multiply 5 and 2 to get 10

y=%28-5%29x%2B10%2B-6Subtract -6 from both sides


y=%28-5%29x%2B4 Combine like terms
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Answer:


So the equation of the line with a slope of -5 which goes through the point (2,-6) is:

y=%28-5%29x%2B4 which is now in y=mx%2Bb form where the slope is m=-5 and the y-intercept is b=4

Notice if we graph the equation y=%28-5%29x%2B4 and plot the point (2,-6), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-5%29x%2B4 through the point (2,-6)
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 (2,-6), this verifies our answer.