SOLUTION: please help how do you write the equation of a line through the given point with the given slope? (6,-6) m=-7/3

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Question 117502This question is from textbook
: please help
how do you write the equation of a line through the given point with the given slope?
(6,-6) m=-7/3 This question is from textbook

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 -7%2F3 which goes through the point (6,-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=%28-7%2F3%29%28x-6%29 Plug in m=-7%2F3, x%5B1%5D=6, and y%5B1%5D=-6 (these values are given)


y%2B6=%28-7%2F3%29%28x-6%29 Rewrite y--6 as y%2B6


y%2B6=%28-7%2F3%29x%2B%28-7%2F3%29%28-6%29 Distribute -7%2F3

y%2B6=%28-7%2F3%29x%2B14 Multiply -7%2F3 and -6 to get 14

y=%28-7%2F3%29x%2B14-6 Subtract 6 from both sides to isolate y

y=%28-7%2F3%29x%2B8 Combine like terms 14 and -6 to get 8
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Answer:


So the equation of the line with a slope of -7%2F3 which goes through the point (6,-6) is:

y=%28-7%2F3%29x%2B8 which is now in y=mx%2Bb form where the slope is m=-7%2F3 and the y-intercept is b=8

Notice if we graph the equation y=%28-7%2F3%29x%2B8 and plot the point (6,-6), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-7%2F3%29x%2B8 through the point (6,-6)
and we can see that the point lies on the line. Since we know the equation has a slope of -7%2F3 and goes through the point (6,-6), this verifies our answer.