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

1 answer

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