Question

write the equation of the line passing through (e^pi, square root of 2) with a slope of pi/6

Answer 1

@Hero

Answer 2

@welshfella

Answer 3

use the point slope formula

y - y1 = m(x - x)

where (x1,y1) is the point on the line and m = the slope

Answer 4

here x1 = e^pi , y1 = sqrt 2 and m = pi/6

Answer 5

so just plug theses values in

Answer 6

but how do i simplify? y2-square root 2=pi/6(x2-e^pi)

Answer 7

\[y-\sqrt{2}=\frac{\pi}{6}(x-e^{\pi})\]
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,
\[a=\pi\]\[b=-6\]\[c=6\sqrt{2}-\pi e^{\pi}\]