Answer :

GinnyAnswer
Certainly! To create a table of values for the equation [tex]\(3x + 2y = 6\)[/tex] with [tex]\(x\)[/tex] values ranging from [tex]\(-1\)[/tex] to [tex]\(3\)[/tex], we need to determine the corresponding [tex]\(y\)[/tex] values. Let's solve for [tex]\(y\)[/tex] by isolating it on one side of the equation:

[tex]\[3x + 2y = 6\][/tex]

Subtract [tex]\(3x\)[/tex] from both sides:

[tex]\[2y = 6 - 3x\][/tex]

Now, divide both sides by 2 to solve for [tex]\(y\)[/tex]:

[tex]\[y = \frac{6 - 3x}{2}\][/tex]

We will substitute the given [tex]\(x\)[/tex] values [tex]\([-1, 0, 1, 2, 3]\)[/tex] into this equation to find the corresponding [tex]\(y\)[/tex] values.

1. For [tex]\(x = -1\)[/tex]:
[tex]\[ y = \frac{6 - 3(-1)}{2} = \frac{6 + 3}{2} = \frac{9}{2} = 4.5 \][/tex]

2. For [tex]\(x = 0\)[/tex]:
[tex]\[ y = \frac{6 - 3 \cdot 0}{2} = \frac{6}{2} = 3 \][/tex]

3. For [tex]\(x = 1\)[/tex]:
[tex]\[ y = \frac{6 - 3 \cdot 1}{2} = \frac{6 - 3}{2} = \frac{3}{2} = 1.5 \][/tex]

4. For [tex]\(x = 2\)[/tex]:
[tex]\[ y = \frac{6 - 3 \cdot 2}{2} = \frac{6 - 6}{2} = \frac{0}{2} = 0 \][/tex]

5. For [tex]\(x = 3\)[/tex]:
[tex]\[ y = \frac{6 - 3 \cdot 3}{2} = \frac{6 - 9}{2} = \frac{-3}{2} = -1.5 \][/tex]

Now, we can create the table of values:

[tex]\[ \begin{array}{c|c} x & y \\ \hline -1 & 4.5 \\ 0 & 3 \\ 1 & 1.5 \\ 2 & 0 \\ 3 & -1.5 \\ \end{array} \][/tex]

So the table of values for the graph of [tex]\(3x + 2y = 6\)[/tex] with [tex]\(x\)[/tex] values ranging from [tex]\(-1\)[/tex] to [tex]\(3\)[/tex] is:

[tex]\[ \begin{array}{c|c} x & y \\ \hline -1 & 4.5 \\ 0 & 3 \\ 1 & 1.5 \\ 2 & 0 \\ 3 & -1.5 \\ \end{array} \][/tex]

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