To fill in the missing values in the table using the equation \( y - 5 = \frac{x}{3} \), we'll rearrange the equation to express \( y \) in terms of \( x \):
\[ y = \frac{x}{3} + 5 \]
Now we can calculate the missing values based on the given \( x \) and \( y \) values.
- For \( y = 1 \): \[ 1 = \frac{x}{3} + 5 \] Subtract 5 from both sides: \[ 1 - 5 = \frac{x}{3} \implies -4 = \frac{x}{3} \] Multiply by 3: \[ x = -12 \]
So, the first row is \( x: -12, y: 1 \).
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For \( x = -3 \), find \( y \): \[ y = \frac{-3}{3} + 5 = -1 + 5 = 4 \] This confirms the value is correct.
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For \( x = 0 \), find \( y \): \[ y = \frac{0}{3} + 5 = 0 + 5 = 5 \]
So, the third row is \( x: 0, y: 5 \).
- For \( x = 6 \), find \( y \): \[ y = \frac{6}{3} + 5 = 2 + 5 = 7 \]
So, the fourth row is \( x: 6, y: 7 \).
- For \( y = 8 \): \[ 8 = \frac{x}{3} + 5 \] Subtract 5 from both sides: \[ 8 - 5 = \frac{x}{3} \implies 3 = \frac{x}{3} \] Multiply by 3: \[ x = 9 \]
So, the last row is \( x: 9, y: 8 \).
Now, compiling everything, the table looks like this:
- \( x: -12, y: 1 \)
- \( x: -3, y: 4 \)
- \( x: 0, y: 5 \)
- \( x: 6, y: 7 \)
- \( x: 9, y: 8 \)
Here are the missing values:
\[ \text{First Row: } x = -12 \ \text{Third Row: } y = 5 \ \text{Fourth Row: } y = 7 \ \text{Fifth Row: } x = 9 \]