f ( x ) = 1 - e^x
We have too find the slope of the graph at the point: f ` ( x o ), where x o is a coordinate of the point where the graph crosses the x-axis ). Also an equation of the tangent line is: y - y o = f ` ( x o ) ( x - x o ) , but we don`t need it here ( we just need to find the slope ).
1 - e ^x = 0
e ^x = 1 => x o = 0
f ` ( x ) = - e ^x
f` ( 0 ) = - e^0 = - 1
The slope is : m = - 1