Question

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

Answer 1

To find the values of \( y \) for the equation \( 4y = -x + 12 \) given the values of \( x \) (which are -8, -4, 0, 4, and 8), we need to first rewrite the equation in terms of \( y \):

\[
y = \frac{-x + 12}{4} = -\frac{1}{4}x + 3
\]

Now we can calculate \( y \) for each given \( x \) value.

1. For \( x = -8 \):
\[
y = -\frac{1}{4}(-8) + 3 = 2 + 3 = 5
\]

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

3. For \( x = 0 \):
\[
y = -\frac{1}{4}(0) + 3 = 0 + 3 = 3
\]

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

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

Now we can summarize the results:

\[
\begin{align*}
x = -8 & \rightarrow y = 5 \\
x = -4 & \rightarrow y = 4 \\
x = 0 & \rightarrow y = 3 \\
x = 4 & \rightarrow y = 2 \\
x = 8 & \rightarrow y = 1 \\
\end{align*}
\]

So the corresponding values of \( (x, y) \) pairs would be:

\[
(-8, 5), (-4, 4), (0, 3), (4, 2), (8, 1)
\]