Step 1 :Given the equation \(x - 2y + 6 = 0\), we can rearrange it to solve for \(y\) in terms of \(x\), which gives us \(y = \frac{x}{2} + 3\).
Step 2 :Using this equation, we can find the \(y\)-values corresponding to given \(x\)-values and vice versa.
Step 3 :For \(x = -1\), we substitute into the equation to get \(y = \frac{-1}{2} + 3 = \frac{5}{2}\). So the ordered pair is \((-1, \frac{5}{2})\).
Step 4 :For \(x = -2\), we substitute into the equation to get \(y = \frac{-2}{2} + 3 = 2\). So the ordered pair is \((-2, 2)\).
Step 5 :For \(y = 1\), we rearrange the equation to solve for \(x\) and substitute \(y = 1\) to get \(x = 2(1) - 6 = -4\). So the ordered pair is \((-4, 1)\).
Step 6 :\(\boxed{\text{Final Answer: The ordered pairs that satisfy the equation } x-2y+6=0 \text{ are } (-1, \frac{5}{2}), (-2, 2), (-4, 1)}\)