The problem involves Mia's allowance and her savings over time. Let's break it down step by step.

Problem:

• Mia starts with $40.
• Each week, she receives $5 as an allowance, which she plans to save.
• We need to find which of the given ordered pairs $(x, y)$ is on Mia's graph, where:
  • $x$ represents the number of weeks.
  • $y$ represents the total amount of money Mia has.

Equation Setup:

Since Mia's savings increase by $5 every week, this is a linear equation problem. The general form of a linear equation is: $y = mx + b$ where:

• $m$ is the rate of change (slope, which is $5 per week),
• $b$ is the starting amount (initial money, which is $40).

Thus, the equation for Mia's total savings is: $y = 5x + 40$

Checking the Ordered Pairs:

Let's plug in the $x$-values from the given ordered pairs and see if the corresponding $y$-values match the equation.

1. $(6, 30)$: $y = 5(6) + 40 = 30 + 40 = 70 \quad (\text{not } 30)$ This is not on the graph.

2. $(2, 80)$: $y = 5(2) + 40 = 10 + 40 = 50 \quad (\text{not } 80)$ This is not on the graph.

3. $(1, 40)$: $y = 5(1) + 40 = 5 + 40 = 45 \quad (\text{not } 40)$ This is not on the graph.

4. $(4, 60)$: $y = 5(4) + 40 = 20 + 40 = 60 \quad (\text{correct})$ This is on the graph.

Conclusion:

The correct ordered pair that is on Mia's graph is (4, 60).

Let me know if you need further details or if you'd like clarification on anything!

Related Questions:

1. How can you determine the slope from a linear equation?
2. What is the significance of the y-intercept in real-life scenarios like this?
3. How would the graph look if Mia saved $10 per week instead of $5?
4. How do you graph the line of an equation like $y = 5x + 40$?
5. How would the equation change if Mia started with $0 instead of $40?

Tip:

In problems involving constant savings or spending over time, always look for a linear relationship where the slope represents the rate of change.