Question

Use the equation y - 6 = x/4 to fill in the missing values in the table below.
X: 32, 12, 0, ___, ___
Y: 14, ___, ___, 4, -3
A) -9
B) -8
C) 6
D) -36
E) 9
F) 12
G) 10

Answer 1

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

\[
y = \frac{x}{4} + 6
\]

Now, we can plug in the given values of \( x \) and calculate \( y \) to find the missing entries and vice versa.

### Given values in the table:

1. **When \( x = 32 \)**:
\[
y = \frac{32}{4} + 6 = 8 + 6 = 14
\]
This entry is consistent with the table.

2. **When \( x = 12 \)**:
\[
y = \frac{12}{4} + 6 = 3 + 6 = 9
\]
We can fill in the first missing value of \( y \) as **9**.

3. **When \( x = 0 \)**:
\[
y = \frac{0}{4} + 6 = 0 + 6 = 6
\]
We can fill in the second missing value of \( y \) as **6**.

4. **When \( y = 4 \)**:
We need to find \( x \) here:
\[
4 - 6 = \frac{x}{4} \implies -2 = \frac{x}{4} \implies x = -8
\]
We can fill in the first missing value of \( x \) as **-8**.

5. **When \( y = -3 \)**:
We need to find \( x \) again:
\[
-3 - 6 = \frac{x}{4} \implies -9 = \frac{x}{4} \implies x = -36
\]
We can fill in the second missing value of \( x \) as **-36**.

### Final filled table:

- X: 32, 12, 0, -8, -36
- Y: 14, 9, 6, 4, -3

### Answers:
- The missing value for \( y \) when \( x = 12 \) is **9**.
- The missing value for \( y \) when \( x = 0 \) is **6**.
- The missing value for \( x \) when \( y = 4 \) is **-8**.
- The missing value for \( x \) when \( y = -3 \) is **-36**.

Therefore, the selections for the missing values from the options provided are:
- A) -9
- B) -8 (Correct)
- C) 6
- D) -36 (Correct)
- E) 9 (Correct)
- F) 12
- G) 10