To find the correct equation that matches Michele's savings scenario, let's analyze the given information.
- After 2 weeks (x = 2), Michele has $55 (y = 55).
- After 7 weeks (x = 7), Michele plans to have $105 (y = 105).
Now, we need to find the change in her savings over time to derive the equation:
- The change in time from 2 weeks to 7 weeks is 5 weeks.
- The change in her savings from $55 to $105 is $105 - $55 = $50.
This means that in those 5 weeks, she is saving $50. Therefore, her weekly savings rate can be calculated as:
\[ \text{Weekly savings} = \frac{50 \text{ dollars}}{5 \text{ weeks}} = 10 \text{ dollars/week} \]
From this, we can establish that Michele starts with $55 and saves $10 for every week after the initial 2 weeks. Therefore, if \( y \) is her total savings and \( x \) is the number of weeks, the relationship can be expressed as:
\[ y - 55 = 10(x - 2) \]
This is the first equation provided.
Now, let's check if this equation is consistent with the points we have:
-
At \( x = 2 \): \[ y - 55 = 10(2 - 2) \implies y - 55 = 0 \implies y = 55 \quad \text{(correct)} \]
-
At \( x = 7 \): \[ y - 55 = 10(7 - 2) \implies y - 55 = 50 \implies y = 105 \quad \text{(correct)} \]
Thus, the correct equation that represents Michele's saving scenario is:
\[ \boxed{y - 55 = 10(x - 2)} \]