anonymous
  • anonymous
write the equation of the line passing through (e^pi, square root of 2) with a slope of pi/6
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
welshfella
  • welshfella
use the point slope formula y - y1 = m(x - x) where (x1,y1) is the point on the line and m = the slope

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welshfella
  • welshfella
here x1 = e^pi , y1 = sqrt 2 and m = pi/6
welshfella
  • welshfella
so just plug theses values in
anonymous
  • anonymous
but how do i simplify? y2-square root 2=pi/6(x2-e^pi)
anonymous
  • anonymous
\[y-\sqrt{2}=\frac{\pi}{6}(x-e^{\pi})\] Although not necessary, a linear equation in 2 variables may be simplified into the form of \[ax+by+c=0\] Let's get rid of that 6 first by multiplying throughout by 6 \[6y-6\sqrt{2}=\pi(x-e^{\pi})\] Now we simply open the parenthesis on the right side \[6y-6\sqrt{2}=\pi x-\pi e^{\pi}\] Now it's a matter of rearranging \[\pi x-6y+6\sqrt{2}-\pi e^{\pi}=0\] This is of the form \[ax+by+c=0\] In this case, \[a=\pi\]\[b=-6\]\[c=6\sqrt{2}-\pi e^{\pi}\]

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