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