To determine which table of values correctly corresponds to the equation [tex]\( c = 3.5b \)[/tex], we need to check each table to see if every value pair [tex]\((b, c)\)[/tex] satisfies the equation.
Let's examine each table one by one:
### Table 1
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Loaves } (b) & \text{Cost } (c) \\
\hline
-2 & -7 \\
0 & 0 \\
2 & 7 \\
4 & 14 \\
\hline
\end{array}
\][/tex]
- For [tex]\( b = -2 \)[/tex], [tex]\( c = -7 \)[/tex]: [tex]\( 3.5 \times -2 = -7 \)[/tex]
- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 2 \)[/tex], [tex]\( c = 7 \)[/tex]: [tex]\( 3.5 \times 2 = 7 \)[/tex]
- For [tex]\( b = 4 \)[/tex], [tex]\( c = 14 \)[/tex]: [tex]\( 3.5 \times 4 = 14 \)[/tex]
All pairs satisfy [tex]\( c = 3.5b \)[/tex].
### Table 2
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Loaves } (b) & \text{Cost } (c) \\
\hline
0 & 0 \\
0.5 & 1.75 \\
1 & 3.5 \\
1.5 & 5.25 \\
\hline
\end{array}
\][/tex]
- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 0.5 \)[/tex], [tex]\( c = 1.75 \)[/tex]: [tex]\( 3.5 \times 0.5 = 1.75 \)[/tex]
- For [tex]\( b = 1 \)[/tex], [tex]\( c = 3.5 \)[/tex]: [tex]\( 3.5 \times 1 = 3.5 \)[/tex]
- For [tex]\( b = 1.5 \)[/tex], [tex]\( c = 5.25 \)[/tex]: [tex]\( 3.5 \times 1.5 = 5.25 \)[/tex]
All pairs satisfy [tex]\( c = 3.5b \)[/tex].
### Table 3
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Loaves } (b) & \text{Cost } (c) \\
\hline
0 & 0 \\
3 & 10.5 \\
6 & 21 \\
9 & 31.5 \\
\hline
\end{array}
\][/tex]
- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 3 \)[/tex], [tex]\( c = 10.5 \)[/tex]: [tex]\( 3.5 \times 3 = 10.5 \)[/tex]
- For [tex]\( b = 6 \)[/tex], [tex]\( c = 21 \)[/tex]: [tex]\( 3.5 \times 6 = 21 \)[/tex]
- For [tex]\( b = 9 \)[/tex], [tex]\( c = 31.5 \)[/tex]: [tex]\( 3.5 \times 9 = 31.5 \)[/tex]
All pairs satisfy [tex]\( c = 3.5b \)[/tex].
### Conclusion
Since all the pairs in each of the three tables satisfy the equation [tex]\( c = 3.5b \)[/tex], all three tables match the equation and include only viable solutions. Therefore, the tables of values that match the equation [tex]\( c = 3.5b \)[/tex] are:
1. Table 1
2. Table 2
3. Table 3
