Carmen opens a savings account after starting her summer job and deposits money into it each month. The graph represents the relationship between y
, the total amount of money in her account, and x
 the number of months since she began saving.
 

 
Which equation best represents the relationship between x
 and y
?​​​​​​​
A.y=50x+100

B.y=100x+50

C.y=−50+100

D.y=100x−50

© 202

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!

Carmen opens a savings account after starting her summer job and deposits money into it each month. The graph represents the relationship between y, the total amount of money in her account, and x, the number of months since she began saving. Which equation best represents the relationship between x and y? A.y=50x+100 B.y=100x+50 C.y=−50+100 D.y=100x−50

Explore how to find the best linear equation representing the relationship between time (months) and the total amount saved in Carmen's account. This problem introduces key concepts such as slope, y-intercept, and linear equations. Suitable for students in Grades 6-8.

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