SOLUTION: How would I write the equation of the line has the indicated slope and contains the indicate point m=1/2 (3,5) ? What equation and could you please show the work I spent 45minutes

Algebra ->  Graphs -> SOLUTION: How would I write the equation of the line has the indicated slope and contains the indicate point m=1/2 (3,5) ? What equation and could you please show the work I spent 45minutes      Log On


   

Question 126123: How would I write the equation of the line has the indicated slope and contains the indicate point m=1/2 (3,5) ? What equation and could you please show the work I spent 45minutes
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 (3,5), 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-5=%281%2F2%29%28x-3%29 Plug in m=1%2F2, x%5B1%5D=3, and y%5B1%5D=5 (these values are given)


y-5=%281%2F2%29x%2B%281%2F2%29%28-3%29 Distribute 1%2F2

y-5=%281%2F2%29x-3%2F2 Multiply 1%2F2 and -3 to get -3%2F2

y=%281%2F2%29x-3%2F2%2B5 Add 5 to both sides to isolate y

y=%281%2F2%29x%2B7%2F2 Combine like terms -3%2F2 and 5 to get 7%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 (3,5) is:

y=%281%2F2%29x%2B7%2F2 which is now in y=mx%2Bb form where the slope is m=1%2F2 and the y-intercept is b=7%2F2

Notice if we graph the equation y=%281%2F2%29x%2B7%2F2 and plot the point (3,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%281%2F2%29x%2B7%2F2 through the point (3,5)
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 (3,5), this verifies our answer.