gradient and directional derivative

[moy1989]

Find the equation of the normal line to the curve e^x * sin y = 2 at the point ( ln 2, pi2). Write your answer in the form y = mx + b.

I found the equation in parametric form to be l(t) = ( ln 2, pi/2 ) + t( 1, 2 ), but I don't know how to convert this to the form y = mx + b.

Thanks for any help.

 

[Deleted member 4993]

Find the equation of the normal line to the curve e^x * sin y = 2 at the point ( ln 2, pi2). Write your answer in the form y = mx + b.

I found the equation in parametric form to be l(t) = ( ln 2, pi/2 ) + t( 1, 2 ),

Can you find two different points (x[sub:21tm5fvs]1[/sub:21tm5fvs],y[sub:21tm5fvs]1[/sub:21tm5fvs]) and (x[sub:21tm5fvs]2[/sub:21tm5fvs],y[sub:21tm5fvs]2[/sub:21tm5fvs]) on this line?

then the slope of the line [sub:21tm5fvs]\(\displaystyle m \, = \, \frac{y_2 - y_1}{x_2 - x_1}\)[/sub:21tm5fvs]

and equation of the line would be:

\(\displaystyle y \, = \, m\cdot x \, - \, (m\cdot x_1 + y_1)\)

but I don't know how to convert this to the form y = mx + b.

Thanks for any help.

 

[moy1989]

Never mind, I see how I did not approach this problem correctly. Thanks for the help.