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.