To solve the given problem, we need to find the corresponding [tex]\( Y \)[/tex] values for each [tex]\( X \)[/tex] value using the equation [tex]\( y = 3x - 2 \)[/tex].
Let's calculate step-by-step for each [tex]\( X \)[/tex]:
1. For [tex]\( X = 0 \)[/tex]:
[tex]\[
y = 3(0) - 2 = 0 - 2 = -2
\][/tex]
2. For [tex]\( X = 1 \)[/tex]:
[tex]\[
y = 3(1) - 2 = 3 - 2 = 1
\][/tex]
3. For [tex]\( X = 2 \)[/tex]:
[tex]\[
y = 3(2) - 2 = 6 - 2 = 4
\][/tex]
4. For [tex]\( X = 3 \)[/tex]:
[tex]\[
y = 3(3) - 2 = 9 - 2 = 7
\][/tex]
Now, we can fill in the table with these values:
[tex]\[
\begin{tabular}{|l|l|}
\hline
X & Y \\
\hline
0 & -2 \\
\hline
1 & 1 \\
\hline
2 & 4 \\
\hline
3 & 7 \\
\hline
\end{tabular}
\][/tex]
So the completed table with the values is:
[tex]\[
\begin{tabular}{|l|l|}
\hline
X & Y \\
\hline
0 & -2 \\
\hline
1 & 1 \\
\hline
2 & 4 \\
\hline
3 & 7 \\
\hline
\end{tabular}
\][/tex]
