SOLUTION: Hi Can I have some finding an equation of the line through (3, 4) with slope 5/6? Thanks

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Question 124533: Hi Can I have some finding an equation of the line through (3, 4) with slope 5/6?
Thanks
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 5%2F6 which goes through the point (3,4), 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-4=%285%2F6%29%28x-3%29 Plug in m=5%2F6, x%5B1%5D=3, and y%5B1%5D=4 (these values are given)


y-4=%285%2F6%29x%2B%285%2F6%29%28-3%29 Distribute 5%2F6

y-4=%285%2F6%29x-5%2F2 Multiply 5%2F6 and -3 to get -5%2F2

y=%285%2F6%29x-5%2F2%2B4 Add 4 to both sides to isolate y

y=%285%2F6%29x%2B3%2F2 Combine like terms -5%2F2 and 4 to get 3%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 5%2F6 which goes through the point (3,4) is:

y=%285%2F6%29x%2B3%2F2 which is now in y=mx%2Bb form where the slope is m=5%2F6 and the y-intercept is b=3%2F2

Notice if we graph the equation y=%285%2F6%29x%2B3%2F2 and plot the point (3,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=%285%2F6%29x%2B3%2F2 through the point (3,4)
and we can see that the point lies on the line. Since we know the equation has a slope of 5%2F6 and goes through the point (3,4), this verifies our answer.