Answer :
To fill out the table of equivalent ratios and plot the points on a coordinate axes, let's determine the missing values by using the information provided.
### Information Given:
- Michael read 12 books in 8 months.
### Calculations:
1. Find the Rate of Books per Month:
- Since Michael reads 12 books in 8 months, we can calculate how many books he reads per month by dividing the total number of books by the number of months.
- Books per month = 12 books / 8 months = 1.5 books per month.
2. Complete the Table:
- For 2 Months:
- To find out how many books Michael reads in 2 months, multiply the rate (1.5 books per month) by 2 months.
- Books read in 2 months = 1.5 books/month * 2 months = 3 books.
- For 18 Books:
- To determine how many months it takes to read 18 books, divide 18 books by the rate of 1.5 books per month.
- Months for 18 books = 18 books / 1.5 books/month = 12 months.
Now, we can fill in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Months & Books \\
\hline
2 & 3 \\
\hline
8 & 12 \\
\hline
12 & 18 \\
\hline
\end{tabular}
\][/tex]
### Plotting the Points:
- We can plot these points on a coordinate grid where the x-axis represents the number of months, and the y-axis represents the number of books:
- (2, 3)
- (8, 12)
- (12, 18)
These points will lie on a straight line, as they are part of the same ratio (a constant rate). This line demonstrates the relationship between the number of months and the number of books read by Michael.
### Information Given:
- Michael read 12 books in 8 months.
### Calculations:
1. Find the Rate of Books per Month:
- Since Michael reads 12 books in 8 months, we can calculate how many books he reads per month by dividing the total number of books by the number of months.
- Books per month = 12 books / 8 months = 1.5 books per month.
2. Complete the Table:
- For 2 Months:
- To find out how many books Michael reads in 2 months, multiply the rate (1.5 books per month) by 2 months.
- Books read in 2 months = 1.5 books/month * 2 months = 3 books.
- For 18 Books:
- To determine how many months it takes to read 18 books, divide 18 books by the rate of 1.5 books per month.
- Months for 18 books = 18 books / 1.5 books/month = 12 months.
Now, we can fill in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Months & Books \\
\hline
2 & 3 \\
\hline
8 & 12 \\
\hline
12 & 18 \\
\hline
\end{tabular}
\][/tex]
### Plotting the Points:
- We can plot these points on a coordinate grid where the x-axis represents the number of months, and the y-axis represents the number of books:
- (2, 3)
- (8, 12)
- (12, 18)
These points will lie on a straight line, as they are part of the same ratio (a constant rate). This line demonstrates the relationship between the number of months and the number of books read by Michael.
