Question

complete the table

4y = - x + 12
x -8 -4 0 4 8
y

Answer 1

To complete the table for the equation \( 4y = -x + 12 \), we need to solve for \( y \) in terms of \( x \):

1. Rearranging the equation:
\[
y = \frac{-x + 12}{4} = -\frac{x}{4} + 3
\]

Now we can calculate the values of \( y \) for each given value of \( x \):

- For \( x = -8 \):
\[
y = -\frac{-8}{4} + 3 = 2 + 3 = 5
\]

- For \( x = -4 \):
\[
y = -\frac{-4}{4} + 3 = 1 + 3 = 4
\]

- For \( x = 0 \):
\[
y = -\frac{0}{4} + 3 = 0 + 3 = 3
\]

- For \( x = 4 \):
\[
y = -\frac{4}{4} + 3 = -1 + 3 = 2
\]

- For \( x = 8 \):
\[
y = -\frac{8}{4} + 3 = -2 + 3 = 1
\]

Now we can summarize the results in a table format:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-8 & 5 \\
-4 & 4 \\
0 & 3 \\
4 & 2 \\
8 & 1 \\
\hline
\end{array}
\]

So the completed table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-8 & 5 \\
-4 & 4 \\
0 & 3 \\
4 & 2 \\
8 & 1 \\
\hline
\end{array}
\]