Layla charges $2 per day, plus a sign-up fee of $3. Notice the sign-up fee represents a fixed value, that's gonna be the constant form of the function. And $2 is the ratio of change of the function, because it a cost per day.
Sam charges $3 per day, without extra fee. So, the ratio of change of this function is $3, and it doesn't have a constant term.

According to the given information, the linear function for Layla is:

$f(x)=2x+3$

Notice that the constant ratio of change is coefficient of the independent variable, that is, because that variable represents days, and each charges $2.

On the other hand, the linear function for Sam is:

$g(x)=3x$

As we said before, this expression doesn't have any constant term, because the charges are flate $3 per day, it's just that rate.

Now, to find the number of days needed to both Layla and Sam earn the same money, we just have to solve the equation $f(x)=g(x)$

$2x+3=3x\\3=3x-2x\\x=3$

Therefore, on day three they are gonna earn the same amount of money.

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