Question

use the equation y-6=x/4 to fill in the missing values in the table below
x y
32. 14
12. __
0. __
__. 4
__. -3

Answer 1

To fill in the missing values in the table using the equation \( y - 6 = \frac{x}{4} \), we first solve for \( y \).

Starting with the equation:
\[
y - 6 = \frac{x}{4}
\]
we can simplify it to:
\[
y = \frac{x}{4} + 6
\]

Now we can use this equation to calculate the missing values in the table for the given \( x \) values.

1. For \( x = 32 \):
\[
y = \frac{32}{4} + 6 = 8 + 6 = 14
\]
(already provided)

2. For \( x = 12 \):
\[
y = \frac{12}{4} + 6 = 3 + 6 = 9
\]

3. For \( x = 0 \):
\[
y = \frac{0}{4} + 6 = 0 + 6 = 6
\]

4. For \( y = 4 \):
We set up the equation to find \( x \):
\[
4 - 6 = \frac{x}{4}
\]
\[
-2 = \frac{x}{4}
\]
Multiplying both sides by 4:
\[
x = -8
\]

5. For \( y = -3 \):
Again, we set up the equation to find \( x \):
\[
-3 - 6 = \frac{x}{4}
\]
\[
-9 = \frac{x}{4}
\]
Multiplying both sides by 4:
\[
x = -36
\]

Now we can fill in the missing values in the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
32 & 14 \\
12 & 9 \\
0 & 6 \\
-8 & 4 \\
-36 & -3 \\
\hline
\end{array}
\]

The completed table is as follows:

\[
\begin{align*}
x &= 32, & y &= 14 \\
x &= 12, & y &= 9 \\
x &= 0, & y &= 6 \\
x &= -8, & y &= 4 \\
x &= -36, & y &= -3 \\
\end{align*}
\]