SOLUTION: Write the equation of the line that passes through point (0,5) with a slope of 9/7 Show all work

Algebra ->  Equations -> SOLUTION: Write the equation of the line that passes through point (0,5) with a slope of 9/7 Show all work      Log On


   

Question 117105: Write the equation of the line that passes through point (0,5) with a slope of 9/7
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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 9%2F7 which goes through the point (0,5), 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=%289%2F7%29%28x-0%29 Plug in m=9%2F7, x%5B1%5D=0, and y%5B1%5D=5 (these values are given)


y-5=%289%2F7%29x%2B%289%2F7%29%28-0%29 Distribute 9%2F7

y-5=%289%2F7%29x%2B0 Multiply 9%2F7 and -0 to get 0

y=%289%2F7%29x%2B0%2B5 Add 5 to both sides to isolate y

y=%289%2F7%29x%2B5 Combine like terms 0 and 5 to get 5
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Answer:


So the equation of the line with a slope of 9%2F7 which goes through the point (0,5) is:

y=%289%2F7%29x%2B5 which is now in y=mx%2Bb form where the slope is m=9%2F7 and the y-intercept is b=5

Notice if we graph the equation y=%289%2F7%29x%2B5 and plot the point (0,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%289%2F7%29x%2B5 through the point (0,5)
and we can see that the point lies on the line. Since we know the equation has a slope of 9%2F7 and goes through the point (0,5), this verifies our answer.