Let's analyze the problem step-by-step.

1. Slope Calculation (Part a):

   • The slope of a line is calculated by the formula: $\text{slope} = \frac{\text{change in y}}{\text{change in x}}$
   • From the graph, we can choose two points. For example, (0, 40) and (10, 80).
   • The change in $y$ (savings in dollars) is $80 - 40 = 40$.
   • The change in $x$ (time in weeks) is $10 - 0 = 10$.
   • So, the slope is: $\text{slope} = \frac{40}{10} = 4$
   • This means that the slope is 4.

   Explanation of the Slope: In this context, the slope represents the rate at which Andre’s savings increase per week. Since the slope is 4, it indicates that Andre’s savings increase by $4 each week.

2. Vertical Intercept Calculation (Part b):

   • The vertical intercept is the point where the line crosses the y-axis (when $x = 0$).
   • From the graph, we can see that when $x = 0$, $y = 40$.
   • Therefore, the vertical intercept is 40.

   Explanation of the Vertical Intercept: In this context, the vertical intercept represents the initial amount of savings in Andre’s bank account. So, Andre started with $40 in his bank account at week 0.

Would you like more detailed explanations or have any specific questions?

Here are five related questions to further understand the concepts:

1. How would the graph look if Andre saved $6 per week instead of $4?
2. What does it mean if the slope of the line is negative in a savings context?
3. How can we interpret the graph if the line is horizontal?
4. If Andre started with $50 instead of $40, how would that affect the vertical intercept?
5. What would be the total savings after 15 weeks if the slope remains the same?

Tip: Remember, the slope in a context like savings can be thought of as the "rate of change" or how fast something is increasing or decreasing.