The image you provided appears to show a math worksheet with questions about equations and modeling relationships. Here's an analysis of the problems:

Question 5:

The savings equation is $S = 12m + 40$, where:

• $S$ represents the amount of money saved.
• $m$ represents the number of months.

You need to calculate values based on this equation and fill in the table.

1. When $m = 1$: $S = 12(1) + 40 = 12 + 40 = 52$

2. When $m = 2$: $S = 12(2) + 40 = 24 + 40 = 64$

3. When $m = 7$: $S = 12(7) + 40 = 84 + 40 = 124$

The table is correctly completed with these values.

Question 6:

This is about modeling the relationship between the cost of piano lessons and the number of lessons using the equation $y = 50x + 30$, where:

• $x$ represents the number of lessons.
• $y$ represents the total cost.

1. When $x = 2$: $y = 50(2) + 30 = 100 + 30 = 130$

2. When $x = 3$: $y = 50(3) + 30 = 150 + 30 = 180$

3. When $x = 4$: $y = 50(4) + 30 = 200 + 30 = 230$

The values are correctly calculated and matched with the table.

Would you like me to elaborate further on the problem-solving process? Here are some questions to deepen your understanding:

1. How can you graph these relationships and what do the slopes represent?
2. What is the significance of the $+40$ or $+30$ in these equations?
3. Could you derive these equations if only the table values were provided?
4. How would the equations change if the rates ($12/month or $50/lesson) were adjusted?
5. Can you think of a real-world example where this type of linear equation applies?

Tip: Always identify what each variable represents and check units when working with equations!