Question

Michele had $55 after 2 weeks of saving money. She plans to have $105 after 7 weeks of saving.which equation matches this scenario?
y - 55 = 10 (x - 2)
y = 7x + 55
10x + 7y = 55
y + 7 = 10 (x + 2)

Answer 1

To analyze the scenario, we need to determine the relationship between the weeks of saving and the amount of money Michele has saved.

1. After 2 weeks (x = 2), Michele has $55 (y = 55).
2. 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:
\[
\boxed{y - 55 = 10 (x - 2)}.
\]