Use the equation y - 6 = x/4 to fill in the missing values in the table below.

Question

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