Simone claims the initial value and y-intercept are the same thing on a graph. is she correct? explain.

It most likely will be the initial value when dealing with a cost/value problem. By convention the initial value is set at 0 time.
For example, an exponential function of interest on a savings account or depreciation of a car. (0 years, initial value) As time progresses the value changes.

If the graph is not of a cost/value problem then it could be something else entirely or if for example you were trying to back calculate the inital value of something and chose the present year as 0 time. Initial value being the y-intercept is more or less determined by how the problem is set up and bit is simplest to set it as so.