To analyze the scenario, we need to determine the relationship between the weeks of saving and the amount of money Michele has saved.
- After 2 weeks (x = 2), Michele has $55 (y = 55).
- After 7 weeks (x = 7), Michele plans to have $105 (y = 105).
We can now find the slope (rate of saving) and create the equation of the line.
First, we calculate the change in amount over the change in weeks:
- From week 2 to week 7 (a change of 5 weeks):
- From $55 to $105 (a change of $50).
The rate of saving per week is: \[ \text{Rate} = \frac{\Delta y}{\Delta x} = \frac{105 - 55}{7 - 2} = \frac{50}{5} = 10 \text{ dollars per week}. \]
So, Michele saves $10 each week.
Given that she had $55 after 2 weeks, we can set up the equation: \[ y - 55 = 10(x - 2) \] This reflects the scenario correctly.
Now, let's look at the choices:
- y - 55 = 10 (x - 2) is our derived equation.
- y = 7x + 55 does not fit our scenario.
- 10x + 7y = 55 does not fit our linear growth with time.
- y + 7 = 10(x + 2) does not match the context of the data.
The correct equation that matches the scenario is: \[ \boxed{y - 55 = 10 (x - 2)}. \]