Answer :
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]
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]
