SOLUTION: Question: Write an equation of the line that passes through each point with the given slope. (2,2),m=1/2

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Question 175489: Question: Write an equation of the line that passes through each point with the given slope. (2,2),m=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 (2,2), 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-2%29 Plug in m=1%2F2, x%5B1%5D=2, and y%5B1%5D=2 (these values are given)


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

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

y=%281%2F2%29x-1%2B2 Add 2 to both sides to isolate y

y=%281%2F2%29x%2B1 Combine like terms -1 and 2 to get 1
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Answer:


So the equation of the line with a slope of 1%2F2 which goes through the point (2,2) is:

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

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

Graph of y=%281%2F2%29x%2B1 through the point (2,2)
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 (2,2), this verifies our answer.