Question

Use the equation: y - 6 = x/4 to fill in the missing values in the BLANK's below
x: 32 y: 14
x: 12 y: BLANK
x: 0 y: BLANK
x: BLANK y: 4
x: BLANK y: -3

Answer 1

To fill in the missing values in the equation \( y - 6 = \frac{x}{4} \), let's rearrange the equation to express \( y \) explicitly:

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

Now, we will use this equation to calculate the missing values for each case provided.

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

**So, \( y = 9 \)**.

### 2. For \( x = 0 \), find \( y \):
\[
y = \frac{0}{4} + 6 = 0 + 6 = 6
\]

**So, \( y = 6 \)**.

### 3. For \( y = 4 \), find \( x \):
Set \( y = 4 \) in the equation:
\[
4 - 6 = \frac{x}{4} \Rightarrow -2 = \frac{x}{4}
\]
Multiply both sides by 4:
\[
x = -8
\]

**So, \( x = -8 \)**.

### 4. For \( y = -3 \), find \( x \):
Set \( y = -3 \) in the equation:
\[
-3 - 6 = \frac{x}{4} \Rightarrow -9 = \frac{x}{4}
\]
Multiply both sides by 4:
\[
x = -36
\]

**So, \( x = -36 \)**.

### Summary of Missing Values:
- For \( x: 12 \), \( y: 9 \)
- For \( x: 0 \), \( y: 6 \)
- For \( x: -8 \), \( y: 4 \)
- For \( x: -36 \), \( y: -3 \)

Final filled out values:
- x: 32, y: 14
- x: 12, y: **9**
- x: 0, y: **6**
- x: **-8**, y: 4
- x: **-36**, y: -3