Problem

Create a table of values for the graph of $3 x+2 y=6$ where the values of $x$ are from -1 to 3 .

Answer

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Answer

\(\boxed{\begin{array}{c|c} x & y \\ \hline -1 & 4.5 \\ 0 & 3.0 \\ 1 & 1.5 \\ 2 & 0.0 \\ 3 & -1.5 \end{array}}\)

Steps

Step 1 :Create a table of values for the given equation, with x values ranging from -1 to 3. To do this, iterate through the x values and solve for y in each case.

Step 2 :\(x = -1\): \(3(-1) + 2y = 6\) => \(2y = 9\) => \(y = 4.5\)

Step 3 :\(x = 0\): \(3(0) + 2y = 6\) => \(2y = 6\) => \(y = 3.0\)

Step 4 :\(x = 1\): \(3(1) + 2y = 6\) => \(2y = 3\) => \(y = 1.5\)

Step 5 :\(x = 2\): \(3(2) + 2y = 6\) => \(2y = 0\) => \(y = 0.0\)

Step 6 :\(x = 3\): \(3(3) + 2y = 6\) => \(2y = -3\) => \(y = -1.5\)

Step 7 :\(\boxed{\begin{array}{c|c} x & y \\ \hline -1 & 4.5 \\ 0 & 3.0 \\ 1 & 1.5 \\ 2 & 0.0 \\ 3 & -1.5 \end{array}}\)

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