To fill in the table with the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values using the equation [tex]\( y = -\frac{5}{2}x + 3 \)[/tex], we will calculate [tex]\( y \)[/tex] step-by-step for each [tex]\( x \)[/tex].
Step 1: Calculate [tex]\( y \)[/tex] when [tex]\( x = -8 \)[/tex]
[tex]\[ y = -\frac{5}{2}(-8) + 3 \][/tex]
[tex]\[ y = \frac{5 \times 8}{2} + 3 \][/tex]
[tex]\[ y = \frac{40}{2} + 3 \][/tex]
[tex]\[ y = 20 + 3 \][/tex]
[tex]\[ y = 23 \][/tex]
So, when [tex]\( x = -8 \)[/tex], [tex]\( y = 23 \)[/tex].
Step 2: Calculate [tex]\( y \)[/tex] when [tex]\( x = -4 \)[/tex]
[tex]\[ y = -\frac{5}{2}(-4) + 3 \][/tex]
[tex]\[ y = \frac{5 \times 4}{2} + 3 \][/tex]
[tex]\[ y = \frac{20}{2} + 3 \][/tex]
[tex]\[ y = 10 + 3 \][/tex]
[tex]\[ y = 13 \][/tex]
So, when [tex]\( x = -4 \)[/tex], [tex]\( y = 13 \)[/tex].
Step 3: Calculate [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]
[tex]\[ y = -\frac{5}{2}(6) + 3 \][/tex]
[tex]\[ y = -\frac{5 \times 6}{2} + 3 \][/tex]
[tex]\[ y = -\frac{30}{2} + 3 \][/tex]
[tex]\[ y = -15 + 3 \][/tex]
[tex]\[ y = -12 \][/tex]
So, when [tex]\( x = 6 \)[/tex], [tex]\( y = -12 \)[/tex].
Summary Table
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
-8 & 23 \\
-4 & 13 \\
6 & -12 \\
\end{array}
\][/tex]
In conclusion:
- When [tex]\( x = -8 \)[/tex], [tex]\( y = 23 \)[/tex].
- When [tex]\( x = -4 \)[/tex], [tex]\( y = 13 \)[/tex].
- When [tex]\( x = 6 \)[/tex], [tex]\( y = -12 \)[/tex].
