Certainly! Let's apply the function rule [tex]\( y = -4x + 3 \)[/tex] to each value of [tex]\( x \)[/tex] to find the corresponding [tex]\( y \)[/tex] values.
### Step-by-Step Calculation:
1. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -4(-1) + 3 = 4 + 3 = 7
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( y = 7 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -4(0) + 3 = 0 + 3 = 3
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = 3 \)[/tex].
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -4(1) + 3 = -4 + 3 = -1
\][/tex]
So, when [tex]\( x = 1 \)[/tex], [tex]\( y = -1 \)[/tex].
4. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -4(2) + 3 = -8 + 3 = -5
\][/tex]
So, when [tex]\( x = 2 \)[/tex], [tex]\( y = -5 \)[/tex].
Given these calculations, we can fill in the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-1 & 7 \\
\hline
0 & 3 \\
\hline
1 & -1 \\
\hline
2 & -5 \\
\hline
\end{tabular}
\][/tex]
