To fill in the table using the given function rule [tex]\( y = -4x + 2 \)[/tex], we need to use this formula to calculate the [tex]\( y \)[/tex]-values corresponding to each [tex]\( x \)[/tex]-value.
Here’s a step-by-step explanation for each [tex]\( x \)[/tex]-value:
1. For [tex]\( x = -1 \)[/tex]:
- Plug [tex]\( x = -1 \)[/tex] into the function:
[tex]\[
y = -4(-1) + 2
\][/tex]
- Calculate the value:
[tex]\[
y = 4 + 2 = 6
\][/tex]
2. For [tex]\( x = 0 \)[/tex]:
- Plug [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
y = -4(0) + 2
\][/tex]
- Calculate the value:
[tex]\[
y = 0 + 2 = 2
\][/tex]
3. For [tex]\( x = 1 \)[/tex]:
- Plug [tex]\( x = 1 \)[/tex] into the function:
[tex]\[
y = -4(1) + 2
\][/tex]
- Calculate the value:
[tex]\[
y = -4 + 2 = -2
\][/tex]
4. For [tex]\( x = 2 \)[/tex]:
- Plug [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
y = -4(2) + 2
\][/tex]
- Calculate the value:
[tex]\[
y = -8 + 2 = -6
\][/tex]
Now that we have calculated the [tex]\( y \)[/tex]-values for each [tex]\( x \)[/tex]-value, we can fill in the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-1 & 6 \\
0 & 2 \\
1 & -2 \\
2 & -6 \\
\hline
\end{tabular}
\][/tex]
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
-1 & 6 \\
0 & 2 \\
1 & -2 \\
2 & -6 \\
\hline
\end{tabular}
\][/tex]
