SOLUTION: Graph the lines with the given property: Goes through (3,3); m = 1/3

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Question 114962: Graph the lines with the given property: Goes through (3,3); m = 1/3
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 1%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=%281%2F3%29%28x-3%29 Plug in m=1%2F3, x%5B1%5D=3, and y%5B1%5D=3 (these values are given)


y-3=%281%2F3%29x%2B%281%2F3%29%28-3%29 Distribute 1%2F3

y-3=%281%2F3%29x-1 Multiply 1%2F3 and -3 to get -1

y=%281%2F3%29x-1%2B3 Add 3 to both sides to isolate y

y=%281%2F3%29x%2B2 Combine like terms -1 and 3 to get 2
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Answer:


So the equation of the line with a slope of 1%2F3 which goes through the point (3,3) is:

y=%281%2F3%29x%2B2 which is now in y=mx%2Bb form where the slope is m=1%2F3 and the y-intercept is b=2

Notice if we graph the equation y=%281%2F3%29x%2B2 and plot the point (3,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=%281%2F3%29x%2B2 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 1%2F3 and goes through the point (3,3), this verifies our answer.