Let's fill in the table step-by-step using the given function rule [tex]\( y = -10x - 3 \)[/tex].
1. For [tex]\( x = -5 \)[/tex]:
- Substitute [tex]\( -5 \)[/tex] into the function:
[tex]\[
y = -10(-5) - 3
\][/tex]
- Calculate the value:
[tex]\[
y = 50 - 3 = 47
\][/tex]
Therefore, when [tex]\( x = -5 \)[/tex], [tex]\( y = 47 \)[/tex].
2. For [tex]\( x = -1 \)[/tex]:
- Substitute [tex]\( -1 \)[/tex] into the function:
[tex]\[
y = -10(-1) - 3
\][/tex]
- Calculate the value:
[tex]\[
y = 10 - 3 = 7
\][/tex]
Therefore, when [tex]\( x = -1 \)[/tex], [tex]\( y = 7 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( 0 \)[/tex] into the function:
[tex]\[
y = -10(0) - 3
\][/tex]
- Calculate the value:
[tex]\[
y = 0 - 3 = -3
\][/tex]
Therefore, when [tex]\( x = 0 \)[/tex], [tex]\( y = -3 \)[/tex].
4. For [tex]\( x = 1 \)[/tex]:
- Substitute [tex]\( 1 \)[/tex] into the function:
[tex]\[
y = -10(1) - 3
\][/tex]
- Calculate the value:
[tex]\[
y = -10 - 3 = -13
\][/tex]
Therefore, when [tex]\( x = 1 \)[/tex], [tex]\( y = -13 \)[/tex].
Now, we can fill in the table with these values:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-5 & 47 \\
\hline
-1 & 7 \\
\hline
0 & -3 \\
\hline
1 & -13 \\
\hline
\end{tabular}
\][/tex]
