Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

For the equation [tex]3x - 2y = -6[/tex]:

a) Complete the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
& \\
\hline
& \\
\hline
0 & \\
\hline
\end{tabular}
\][/tex]


Sagot :

To solve the given equation [tex]\(3x - 2y = -6\)[/tex] and complete the table, we'll determine the values of [tex]\(y\)[/tex] at specific [tex]\(x\)[/tex] values. Here are the steps we'll follow:

1. Rearrange the equation to solve for [tex]\(y\)[/tex]:
[tex]\[3x - 2y = -6 \quad \Rightarrow \quad -2y = -3x - 6 \quad \Rightarrow \quad y = \frac{3x + 6}{2}\][/tex]

2. Substitute the [tex]\(x\)[/tex] values into the equation and calculate the corresponding [tex]\(y\)[/tex] values.

Let's fill in the table for [tex]\(x\)[/tex] values from [tex]\(-2\)[/tex] to [tex]\(2\)[/tex], including [tex]\(x = 0\)[/tex]:

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

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

3. When [tex]\(x = 0\)[/tex]:
[tex]\[y = \frac{3(0) + 6}{2} = \frac{0 + 6}{2} = \frac{6}{2} = 3\][/tex]

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

5. When [tex]\(x = 2\)[/tex]:
[tex]\[y = \frac{3(2) + 6}{2} = \frac{6 + 6}{2} = \frac{12}{2} = 6\][/tex]

Now we can complete the table:

[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline -2 & 0.0 \\ \hline -1 & 1.5 \\ \hline 0 & 3.0 \\ \hline 1 & 4.5 \\ \hline 2 & 6.0 \\ \hline \end{tabular} \][/tex]

This completes the table for the given equation [tex]\(3x - 2y = -6\)[/tex].