Problem

Use the equation to complete the table. Use the table to list some of the ordered pairs that satisfy the equation.
\[
x-2 y+6=0
\]
\begin{tabular}{|c|c|c|}
\hline $\mathbf{x}$ & $\mathbf{y}$ & $(\mathbf{x}, \mathbf{y})$ \\
\hline-1 & $\square$ & $\square$ \\
\hline$\square$ & 1 & $\square$ \\
\hline-2 & $\square$ & $\square$ \\
\hline
\end{tabular}

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{\text{Final Answer: The ordered pairs that satisfy the equation } x-2y+6=0 \text{ are } (-1, \frac{5}{2}), (-2, 2), (-4, 1)}\)

Steps

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 :\(\boxed{\text{Final Answer: The ordered pairs that satisfy the equation } x-2y+6=0 \text{ are } (-1, \frac{5}{2}), (-2, 2), (-4, 1)}\)

link_gpt