Sure! Let's find the values of [tex]\( y \)[/tex] for the given values of [tex]\( x \)[/tex] according to the equation [tex]\( y = 5x \)[/tex]. Here are the steps:
1. Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[
y = 5(-1) = -5
\][/tex]
So, [tex]\( A = -5 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[
y = 5(0) = 0
\][/tex]
So, [tex]\( B = 0 \)[/tex].
3. Substitute [tex]\( x = 1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[
y = 5(1) = 5
\][/tex]
So, [tex]\( C = 5 \)[/tex].
4. Substitute [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[
y = 5(2) = 10
\][/tex]
So, [tex]\( D = 10 \)[/tex].
Now we can complete the table as follows:
[tex]\[
\begin{tabular}{c|c|c|c|c}
$x$ & -1 & 0 & 1 & 2 \\
\hline
$y$ & -5 & 0 & 5 & 10 \\
\end{tabular}
\][/tex]
Therefore, the completed table is:
[tex]\[
\begin{tabular}{c|c|c|c|c}
$x$ & -1 & 0 & 1 & 2 \\
\hline
$y$ & -5 & 0 & 5 & 10 \\
\end{tabular}
\][/tex]
