SOLUTION: graph the line with the slope 2/3 passing through the point (-2,1)

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Question 124725: graph the line with the slope 2/3 passing through the point (-2,1)
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 (-2,1), 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-1=%282%2F3%29%28x--2%29 Plug in m=2%2F3, x%5B1%5D=-2, and y%5B1%5D=1 (these values are given)


y-1=%282%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-1=%282%2F3%29x%2B%282%2F3%29%282%29 Distribute 2%2F3

y-1=%282%2F3%29x%2B4%2F3 Multiply 2%2F3 and 2 to get 4%2F3

y=%282%2F3%29x%2B4%2F3%2B1 Add 1 to both sides to isolate y

y=%282%2F3%29x%2B7%2F3 Combine like terms 4%2F3 and 1 to get 7%2F3 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line with a slope of 2%2F3 which goes through the point (-2,1) is:

y=%282%2F3%29x%2B7%2F3 which is now in y=mx%2Bb form where the slope is m=2%2F3 and the y-intercept is b=7%2F3

Notice if we graph the equation y=%282%2F3%29x%2B7%2F3 and plot the point (-2,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=%282%2F3%29x%2B7%2F3 through the point (-2,1)
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 (-2,1), this verifies our answer.