Certainly! Let's use the given equation [tex]\( y = -670 + 33x \)[/tex] to complete the table and find the missing values.
Here are the steps we will follow:
1. Calculate the missing [tex]\( y \)[/tex]-value when [tex]\( x = 41 \)[/tex].
Given [tex]\( y = -670 + 33x \)[/tex]:
- For [tex]\( x = 41 \)[/tex]:
[tex]\[
y = -670 + 33 \times 41 = -670 + 1353 = 683
\][/tex]
So, when [tex]\( x = 41 \)[/tex], [tex]\( y = 683 \)[/tex].
2. Identify the [tex]\( x \)[/tex]-value that matches the [tex]\( y \)[/tex]-values given.
From the table, notice that:
- For [tex]\( x = 40 \)[/tex], [tex]\( y = 650 \)[/tex]
- For [tex]\( x = 41 \)[/tex], [tex]\( y = 683 \)[/tex]
- For [tex]\( x = 42 \)[/tex], [tex]\( y = 716 \)[/tex]
- For [tex]\( x = 43 \)[/tex], [tex]\( y = 749 \)[/tex]
- For [tex]\( x = 44 \)[/tex], [tex]\( y = 782 \)[/tex]
We need to match the given known values carefully:
- [tex]\( y = 650 \)[/tex] matches with [tex]\( x = 40 \)[/tex]
- [tex]\( y = 683 \)[/tex] matches with [tex]\( x = 42 \)[/tex] instead of [tex]\( x = 41 \)[/tex]. Here we noticed some mismatch in the given values.
Given that we have:
- [tex]\( x = 40 \rightarrow y = 650\)[/tex]
- [tex]\( x = 42 \rightarrow y = 683\)[/tex]
- [tex]\( x = 43 \rightarrow y = 716\)[/tex]
- [tex]\( x = 44 \rightarrow y = 749 \)[/tex]
Clearly seeing the pattern [tex]\( y \)[/tex] values are one step back to there x-values correctly:
Thus the missing [tex]\( x \)[/tex]-value will be clearly [tex]\( y=682 \rightarrow \boxed{x=42}\)[/tex]
The corrected table is:
\begin{tabular}{|c|c|}
\hline
[tex]\( x \)[/tex]-value & [tex]\( y \)[/tex]-value \\
\hline
40 & 650 \\
\hline
41 & 683 \\
\hline
42 & 716 \\
\hline
43 & 749 \\
\hline
44 & 782 \\
\hline
\end{tabular}
Thus, the most accurate table with such questions easily verifies the process for completeness. We correctly identify input/output lies correctly.
