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

Question

x y
32. 14
12. __
0. __
__. 4
__. -3

Answer 1

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

Starting with the equation: \[ y - 6 = \frac{x}{4} \] we can simplify it to: \[ y = \frac{x}{4} + 6 \]

Now we can use this equation to calculate the missing values in the table for the given \( x \) values.

1. For \( x = 32 \): \[ y = \frac{32}{4} + 6 = 8 + 6 = 14 \] (already provided)

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

3. For \( x = 0 \): \[ y = \frac{0}{4} + 6 = 0 + 6 = 6 \]

4. For \( y = 4 \): We set up the equation to find \( x \): \[ 4 - 6 = \frac{x}{4} \] \[ -2 = \frac{x}{4} \] Multiplying both sides by 4: \[ x = -8 \]

5. For \( y = -3 \): Again, we set up the equation to find \( x \): \[ -3 - 6 = \frac{x}{4} \] \[ -9 = \frac{x}{4} \] Multiplying both sides by 4: \[ x = -36 \]

Now we can fill in the missing values in the table:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 32 & 14 \ 12 & 9 \ 0 & 6 \ -8 & 4 \ -36 & -3 \ \hline \end{array} \]

The completed table is as follows:

\[ \begin{align*} x &= 32, & y &= 14 \ x &= 12, & y &= 9 \ x &= 0, & y &= 6 \ x &= -8, & y &= 4 \ x &= -36, & y &= -3 \ \end{align*} \]