Question: Complete the table for the equation $5x - 4y = 20$, and graph the equation. \[…

Complete the table for the equation $5x - 4y = 20$, and graph the equation.

\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -5 \\ \hline 4 & 0 \\ \hline -4 & -10 \\ \hline 8 & 5 \\ \hline \end{array} \]

Use the graphing tool to graph the line using two points.

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Solution

To complete the table for the equation \(5x - 4y = 20\), we’ll substitute the given \(x\) or \(y\) values and solve for the missing variables. For \(x = 0\): Substitute \(x = 0\) into the equation: \[ 5(0) - 4y = 20 \] Simplify: \[ -4y = 20 \] Divide by \(-4\): \[ y = -5 \] For \(y = 0\): Substitute \(y = 0\) into the equation: \[ 5x - 4(0) = 20 \] Simplify: \[ 5x = 20 \] Divide by \(5\): \[ x = 4 \] For \(x = -4\): Substitute \(x = -4\) into the equation: \[ 5(-4) - 4y = 20 \] Simplify: \[ -20 - 4y = 20 \] Add \(20\) to both sides: \[ -4y = 40 \] Divide by \(-4\): \[ y = -10 \] For \(x = 8\): Substitute \(x = 8\) into the equation: \[ 5(8) - 4y = 20 \] Simplify: \[ 40 - 4y = 20 \] Subtract \(40\) from both sides: \[ -4y = -20 \] Divide by \(-4\): \[ y = 5 \] The completed table is: \[ \begin{array}{c|c} x & y \\ \hline 0 & -5 \\ 4 & 0 \\ -4 & -10 \\ 8 & 5 \\ \end{array} \] Use two points, such as \((0, -5)\) and \((4, 0)\), to graph the equation on the graphing tool.