SOLUTION: graph of the line through (3, 2) with slope 1/2

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Question 151369: graph of the line through (3, 2) with slope 1/2
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 1%2F2 which goes through the point (3,2), 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=%281%2F2%29%28x-3%29 Plug in m=1%2F2, x%5B1%5D=3, and y%5B1%5D=2 (these values are given)


y-2=%281%2F2%29x%2B%281%2F2%29%28-3%29 Distribute 1%2F2

y-2=%281%2F2%29x-3%2F2 Multiply 1%2F2 and -3 to get -3%2F2

y=%281%2F2%29x-3%2F2%2B2 Add 2 to both sides to isolate y

y=%281%2F2%29x%2B1%2F2 Combine like terms -3%2F2 and 2 to get 1%2F2 (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 1%2F2 which goes through the point (3,2) is:

y=%281%2F2%29x%2B1%2F2 which is now in y=mx%2Bb form where the slope is m=1%2F2 and the y-intercept is b=1%2F2

Notice if we graph the equation y=%281%2F2%29x%2B1%2F2 and plot the point (3,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%281%2F2%29x%2B1%2F2 through the point (3,2)
and we can see that the point lies on the line. Since we know the equation has a slope of 1%2F2 and goes through the point (3,2), this verifies our answer.