Questions: Complete the table for the equation (2 x-3 y=6), and graph the equation. (x) (y) ------ 0 -2 3 0 6 2 (square) -4

Transcript text: Complete the table for the equation $2 x-3 y=6$, and graph the equation. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 0 & -2 \\ \hline 3 & 0 \\ \hline 6 & 2 \\ \hline$\square$ & -4 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Solve for the missing value in the table

Given the equation $2x - 3y = 6$, we need to find the value of $x$ when $y = -4$.

\[ 2x - 3(-4) = 6 \]

\[ 2x + 12 = 6 \]

\[ 2x = 6 - 12 \]

\[ 2x = -6 \]

\[ x = -3 \]

Step 2: Summarize the table

The completed table is:

\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -2 \\ \hline 3 & 0 \\ \hline 6 & 2 \\ \hline -3 & -4 \\ \hline \end{array} \]

Final Answer

The missing value in the table is $x = -3$.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 7, "ymin": -5, "ymax": 5}, "commands": ["y = (2/3)x - 2"], "latex_expressions": ["$2x - 3y = 6$"]}

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