Let's analyze the information given and the relationships observed.
Charlie bikes 9 miles every day. Looking at the table provided:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Days $(d)$ & 1 & 2 & 3 & 4 & 5 \\
\hline
Miles $(m)$ & 9 & 18 & 27 & 36 & 45 \\
\hline
\end{tabular}
\][/tex]
It is evident that each day's miles can be expressed as follows:
- On day 1: [tex]\( m = 9 \times 1 = 9 \)[/tex]
- On day 2: [tex]\( m = 9 \times 2 = 18 \)[/tex]
- On day 3: [tex]\( m = 9 \times 3 = 27 \)[/tex]
- On day 4: [tex]\( m = 9 \times 4 = 36 \)[/tex]
- On day 5: [tex]\( m = 9 \times 5 = 45 \)[/tex]
From this pattern, we can observe a linear relationship between the number of days ([tex]\(d\)[/tex]) and the miles ([tex]\(m\)[/tex]). For each day, the miles are a multiple of 9 times the days.
To express this relationship algebraically, we see that:
[tex]\[ m = 9 \times d \][/tex]
Thus, the equation that models the situation must be:
[tex]\[ 9d = m \][/tex]
or more formally written as:
[tex]\[ m = 9d \][/tex]
Matching this with the choices provided:
1. [tex]\( 9 = dm \)[/tex]
2. [tex]\( d = 9m \)[/tex]
3. [tex]\( 9d = m \)[/tex]
4. [tex]\( d = 9 + m \)[/tex]
The correct equation that models this situation is:
[tex]\[ \boxed{9d = m} \][/tex]
