SOLUTION: Find an equation of the line satisfying the given conditions. Through (0, 2); m=3/2

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Question 151613: Find an equation of the line satisfying the given conditions.
Through (0, 2); m=3/2
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 3%2F2 which goes through the point (0,2), 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-2=%283%2F2%29%28x-0%29 Plug in m=3%2F2, x%5B1%5D=0, and y%5B1%5D=2 (these values are given)


y-2=%283%2F2%29x%2B%283%2F2%29%28-0%29 Distribute 3%2F2

y-2=%283%2F2%29x%2B0 Multiply 3%2F2 and -0 to get 0

y=%283%2F2%29x%2B0%2B2 Add 2 to both sides to isolate y

y=%283%2F2%29x%2B2 Combine like terms 0 and 2 to get 2
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Answer:


So the equation of the line with a slope of 3%2F2 which goes through the point (0,2) is:

y=%283%2F2%29x%2B2 which is now in y=mx%2Bb form where the slope is m=3%2F2 and the y-intercept is b=2

Notice if we graph the equation y=%283%2F2%29x%2B2 and plot the point (0,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%283%2F2%29x%2B2 through the point (0,2)
and we can see that the point lies on the line. Since we know the equation has a slope of 3%2F2 and goes through the point (0,2), this verifies our answer.