Question: Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the…

Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the points from your table.

\[ -2x - 3y = -9 \]

\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & \\ \hline 0 & \\ \hline 3 & \\ \hline \end{array} \]

Solution

To fill in the table for the equation \(-2x - 3y = -9\), we’ll solve for \(y\) using the given \(x\) values. 1. For \(x = -3\): Substitute \(x = -3\) into the equation: \[ -2(-3) - 3y = -9 \] Simplify: \[ 6 - 3y = -9 \] Subtract 6 from both sides: \[ -3y = -15 \] Divide by -3: \[ y = 5 \] 2. For \(x = 0\): Substitute \(x = 0\) into the equation: \[ -2(0) - 3y = -9 \] Simplify: \[ -3y = -9 \] Divide by -3: \[ y = 3 \] 3. For \(x = 3\): Substitute \(x = 3\) into the equation: \[ -2(3) - 3y = -9 \] Simplify: \[ -6 - 3y = -9 \] Add 6 to both sides: \[ -3y = -3 \] Divide by -3: \[ y = 1 \] The completed table is: \[ \begin{cases} x = -3, & y = 5 \\ x = 0, & y = 3 \\ x = 3, & y = 1 \\ \end{cases} \] You can now plot these points \((-3, 5)\), \((0, 3)\), and \((3, 1)\) on a graph to draw the line.