https://file.aiquickdraw.com/mathbot/file/17290937901865yk0v42c.jpg

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=−50+100

B.y=100x+50

C.y=50x+100

D.y=100x−50


To find the correct equation that represents the relationship between $x$ (months) and $y$ (money saved), we can interpret the graph step by step.

### Observations from the graph:
1. **Initial value (y-intercept)**: At $x = 0$ (when no months have passed), the amount of money saved is $50. This means that the y-intercept is 50.
   
2. **Rate of saving (slope)**: The graph shows a consistent, linear increase in the amount of money saved over time. From month 1 to month 2, the amount saved increases from $150 to $250, which gives a change in $y$ of $100 over a change in $x$ of 1 month. This indicates that Carmen saves $100 per month, which gives a slope of 100.

### The equation of a line is given by:
\[
y = mx + b
\]
Where $m$ is the slope and $b$ is the y-intercept.

### Substituting the values:
- Slope $m = 100$
- Y-intercept $b = 50$

So the equation becomes:
\[
y = 100x + 50
\]

### Therefore, the correct answer is **B. $ y = 100x + 50 $**.

Let me know if you want more details or have any questions!

Here are some related questions:
1. How would the graph change if Carmen saved more money per month?
2. What would the equation look like if the initial savings were $0?
3. How would the slope change if the savings rate doubled?
4. How can you calculate the total money saved after 6 months using the equation?
5. What other factors could influence the shape of the savings graph over time?

**Tip:** The slope of a graph shows the rate of change—here, it represents how much money Carmen saves per month.

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?

Discover how to determine the correct linear equation that models Carmen's monthly savings based on the provided graph. Learn about the slope-intercept form y = mx + b, the slope of 100, and the y-intercept of 50. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation