Final answer:
The equation of the line that is tangent to the graph of y=eˣ is y - 1 = eˣ(x - 0).
Step-by-step explanation:
Since the line is tangent to the graph of y=eˣ, it means that the line touches the graph at only one point without crossing it. To find the equation of this line, we need to determine its slope and a point that lies on the graph.
The slope of the tangent line to the graph of y=eˣ is equal to the derivative of y=eˣ. Taking the derivative, we get dy/dx=eˣ. Now we can evaluate dy/dx at the point where the line touches the graph. Since e^0 = 1, this implies that the point of tangency is (0, 1).
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point on the graph and m is the slope of the tangent line, we can substitute the values into the equation to find the equation of the line:
y - 1 = eˣ(x - 0)