Questions: Complete the three ordered pairs so that they are solutions to the equation y = 1/6 x + 2. x y 6 12 18

Transcript text: Complete the three ordered pairs so that they are solutions to the equation $y=\frac{1}{6} x+2$. \begin{tabular}{c|c} $\mathbf{x}$ & $\mathbf{y}$ \\ \hline 6 & \\ \hline 12 & \\ \hline 18 & \end{tabular}

Solution

Solution Steps

To complete the ordered pairs, substitute each given $ x $ value into the equation $ y = \frac{1}{6}x + 2 $ to find the corresponding $ y $ value.

Step 1: Substitute $ x = 6 $

For $ x = 6 $: \[ y = \frac{1}{6}(6) + 2 = 1 + 2 = 3 \] Thus, the ordered pair is $ (6, 3) $.

Step 2: Substitute $ x = 12 $

For $ x = 12 $: \[ y = \frac{1}{6}(12) + 2 = 2 + 2 = 4 \] Thus, the ordered pair is $ (12, 4) $.

Step 3: Substitute $ x = 18 $

For $ x = 18 $: \[ y = \frac{1}{6}(18) + 2 = 3 + 2 = 5 \] Thus, the ordered pair is $ (18, 5) $.

Final Answer

The complete ordered pairs that are solutions to the equation $ y = \frac{1}{6}x + 2 $ are: \[ \boxed{(6, 3), (12, 4), (18, 5)} \]

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