Question

For what x-values does y=e^-x have the same slop as x+4y = 1

I am not sure what steps I am supposed to take to tackle this problem.

Answer 1

dy/dx = - e^-x , which is also the slope of the tangent at any point (x,y)
slope of x + 4y = 1 is -1/4

so
- e^(-x) = - 1/4
1/e^x = 1/4
e^x = 4

x = ln4