Simone claims that initial value and y-intercept are the same thing. is she correct? why or why not?

Hey there, Belugablaze!
Let's look at our slope intercept formula.
y = mx+b
The initial value would be b, but it is also the y-intercept graphically, as the mx only accounts for the lope and the x values. Let's try an example.

Ex. Admission to the fair costs $45 plus $67 per person. Write a linear equation.

We have:
y = 67(times the number of people) plus 45(initial value, upfront cost)
The 45 is where the line would cross the y axis.
Hope this helps!