To find an equation that matches Michele's saving scenario, we can determine a few key components from the data given:
- After 2 weeks (x = 2), Michele has $55 (y = 55).
- After 7 weeks (x = 7), Michele plans to have $105 (y = 105).
From this, we can calculate Michele's weekly savings:
The difference in weeks from 2 to 7 is 5 weeks, and the difference in her savings from $55 to $105 is: \[ 105 - 55 = 50. \] So, her savings per week is: \[ \text{Savings per week} = \frac{50}{5} = 10. \]
Now we can create a linear equation based on this information. The general form of a linear equation for savings can be represented as: \[ y = mx + b, \] where \(m\) is the slope (weekly savings), and \(b\) is the initial amount saved after some time.
Here, \(m = 10\) (she saves $10 a week), and we know that after 2 weeks she has $55, which can help us find \(b\).
Using the point (2, 55): \[ 55 = 10(2) + b \ 55 = 20 + b \ b = 55 - 20 \ b = 35. \]
So the equation for her total savings over x weeks is: \[ y = 10x + 35. \]
Now, to match this with the provided equations:
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\(y - 55 = 10(x - 2)\)
- Rearranging this gives: \[ y = 10(x - 2) + 55 \ y = 10x - 20 + 55 \ y = 10x + 35. \] This equation is equivalent to what we derived.
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\(y = 7x + 55\) is incorrect as slope does not match.
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\(10x + 7y = 55\) is not in the correct form.
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\(y + 7 = 10(x + 2)\) is not equivalent either.
Therefore, the correct answer is: \[ \boxed{y - 55 = 10(x - 2)}. \]