Certainly! Let's find the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values using the linear equation [tex]\( y = -6x - 3 \)[/tex].
Given the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & \square \\
\hline
-1 & \square \\
\hline
0 & \square \\
\hline
1 & \square \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution
1. For [tex]\( x = -5 \)[/tex]:
Substitute [tex]\( x = -5 \)[/tex] into the equation [tex]\( y = -6x - 3 \)[/tex]:
[tex]\[
y = -6(-5) - 3
\][/tex]
Simplify inside the parentheses:
[tex]\[
y = 30 - 3
\][/tex]
Finally, subtract 3:
[tex]\[
y = 27
\][/tex]
2. For [tex]\( x = -1 \)[/tex]:
Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = -6x - 3 \)[/tex]:
[tex]\[
y = -6(-1) - 3
\][/tex]
Simplify inside the parentheses:
[tex]\[
y = 6 - 3
\][/tex]
Finally, subtract 3:
[tex]\[
y = 3
\][/tex]
3. For [tex]\( x = 0 \)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = -6x - 3 \)[/tex]:
[tex]\[
y = -6(0) - 3
\][/tex]
Multiply by zero and subtract 3:
[tex]\[
y = -3
\][/tex]
4. For [tex]\( x = 1 \)[/tex]:
Substitute [tex]\( x = 1 \)[/tex] into the equation [tex]\( y = -6x - 3 \)[/tex]:
[tex]\[
y = -6(1) - 3
\][/tex]
Simplify inside the parentheses:
[tex]\[
y = -6 - 3
\][/tex]
Finally, add the negative numbers:
[tex]\[
y = -9
\][/tex]
Now, we can fill in the table with the calculated values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 27 \\
\hline
-1 & 3 \\
\hline
0 & -3 \\
\hline
1 & -9 \\
\hline
\end{array}
\][/tex]
