To determine which equation best represents the relationship between $x$ (the number of months) and $y$ (the total amount of money in Carmen's account), let's break down the components typically seen in a linear equation of the form:

$y = mx + b$

Where:

• $m$ is the slope of the line (rate of change, representing the amount Carmen deposits each month).
• $b$ is the y-intercept (the starting amount in Carmen's account when $x = 0$).

Now, let's analyze the options:

• Option A: $y = 50x + 100$

  • The slope is 50, meaning Carmen deposits $50 per month.
  • The y-intercept is 100, meaning she starts with $100 in her account.

• Option B: $y = 100x + 50$

  • The slope is 100, meaning Carmen deposits $100 per month.
  • The y-intercept is 50, meaning she starts with $50 in her account.

• Option C: $y = -50 + 100$

  • This doesn't follow the correct format of a linear equation since it lacks the variable $x$.

• Option D: $y = 100x - 50$

  • The slope is 100, meaning Carmen deposits $100 per month.
  • The y-intercept is -50, which suggests she starts with a debt of $50.

Conclusion:

The correct equation depends on how much Carmen starts with (y-intercept) and how much she deposits per month (slope). If Carmen's graph shows she deposits $50 per month and starts with $100, then Option A $y = 50x + 100$ is the correct answer.

Let me know if you'd like further clarification or have questions on how to verify this from a graph.

Related Questions:

1. What does the slope represent in a savings account graph?
2. How do you calculate the y-intercept from a graph?
3. What is the significance of a negative y-intercept in a financial graph?
4. How would the equation change if Carmen increased her monthly deposit?
5. How can we interpret a linear equation where the slope is zero?

Tip:

When analyzing linear equations in word problems, always check the meaning of the slope and y-intercept to match real-life context!