Let's calculate the values of [tex]\( y \)[/tex] for the given equation [tex]\( y = -\frac{2}{3}x - 1 \)[/tex] at the specified [tex]\( x \)[/tex]-values: [tex]\(-6\)[/tex], [tex]\(3\)[/tex], and [tex]\(9\)[/tex].
### Step-by-Step Solution
#### For [tex]\( x = -6 \)[/tex]:
1. Substitute [tex]\( x = -6 \)[/tex] into the equation:
[tex]\[
y = -\frac{2}{3}(-6) - 1
\][/tex]
2. Calculate the multiplication:
[tex]\[
-\frac{2}{3} \times (-6) = 4
\][/tex]
3. Now subtract 1:
[tex]\[
y = 4 - 1 = 3
\][/tex]
Therefore, when [tex]\( x = -6 \)[/tex], [tex]\( y = 3 \)[/tex].
#### For [tex]\( x = 3 \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = -\frac{2}{3}(3) - 1
\][/tex]
2. Calculate the multiplication:
[tex]\[
-\frac{2}{3} \times 3 = -2
\][/tex]
3. Now subtract 1:
[tex]\[
y = -2 - 1 = -3
\][/tex]
Therefore, when [tex]\( x = 3 \)[/tex], [tex]\( y = -3 \)[/tex].
#### For [tex]\( x = 9 \)[/tex]:
1. Substitute [tex]\( x = 9 \)[/tex] into the equation:
[tex]\[
y = -\frac{2}{3}(9) - 1
\][/tex]
2. Calculate the multiplication:
[tex]\[
-\frac{2}{3} \times 9 = -6
\][/tex]
3. Now subtract 1:
[tex]\[
y = -6 - 1 = -7
\][/tex]
Therefore, when [tex]\( x = 9 \)[/tex], [tex]\( y = -7 \)[/tex].
### Summary Table
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
-6 & 3 \\
3 & -3 \\
9 & -7 \\
\end{array}
\][/tex]
