SOLUTION: Find an equation of the line with the given slope and containing the given point. Slope= 2/3; (-3,3)

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Question 222940: Find an equation of the line with the given slope and containing the given point.
Slope= 2/3; (-3,3)
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%2F3 which goes through the point (-3,3), 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-3=%282%2F3%29%28x--3%29 Plug in m=2%2F3, x%5B1%5D=-3, and y%5B1%5D=3 (these values are given)


y-3=%282%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-3=%282%2F3%29x%2B%282%2F3%29%283%29 Distribute 2%2F3

y-3=%282%2F3%29x%2B2 Multiply 2%2F3 and 3 to get 2

y=%282%2F3%29x%2B2%2B3 Add 3 to both sides to isolate y

y=%282%2F3%29x%2B5 Combine like terms 2 and 3 to get 5
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Answer:


So the equation of the line with a slope of 2%2F3 which goes through the point (-3,3) is:

y=%282%2F3%29x%2B5 which is now in y=mx%2Bb form where the slope is m=2%2F3 and the y-intercept is b=5

Notice if we graph the equation y=%282%2F3%29x%2B5 and plot the point (-3,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=%282%2F3%29x%2B5 through the point (-3,3)
and we can see that the point lies on the line. Since we know the equation has a slope of 2%2F3 and goes through the point (-3,3), this verifies our answer.