Complete the remainder of the table for the given function rule:

[tex]\[ y = 4 - \frac{3x}{4} \][/tex]

[tex]\[
\begin{tabular}{c|ccccc}
$x$ & -4 & 0 & 4 & 8 & 12 \\
\hline
$y$ & 7 & 4 & [?] & [?] & [?] \\
\end{tabular}
\][/tex]



Answer :

Certainly! Let's complete the table step by step according to the given function rule [tex]\( y = 4 - \frac{3}{4} x \)[/tex].

1. Determine [tex]\( y \)[/tex] when [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4 - \frac{3}{4} \times 4 \][/tex]
Substituting [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4 - \frac{3 \times 4}{4} = 4 - 3 = 1 \][/tex]
Thus, when [tex]\( x = 4 \)[/tex], [tex]\( y = 1 \)[/tex].

2. Determine [tex]\( y \)[/tex] when [tex]\( x = 8 \)[/tex]:
[tex]\[ y = 4 - \frac{3}{4} \times 8 \][/tex]
Substituting [tex]\( x = 8 \)[/tex]:
[tex]\[ y = 4 - \frac{3 \times 8}{4} = 4 - 6 = -2 \][/tex]
Thus, when [tex]\( x = 8 \)[/tex], [tex]\( y = -2 \)[/tex].

3. Determine [tex]\( y \)[/tex] when [tex]\( x = 12 \)[/tex]:
[tex]\[ y = 4 - \frac{3}{4} \times 12 \][/tex]
Substituting [tex]\( x = 12 \)[/tex]:
[tex]\[ y = 4 - \frac{3 \times 12}{4} = 4 - 9 = -5 \][/tex]
Thus, when [tex]\( x = 12 \)[/tex], [tex]\( y = -5 \)[/tex].

Now, let's fill in the table with these values:

[tex]\[ \begin{tabular}{c|ccccc} $x$ & -4 & 0 & 4 & 8 & 12 \\ \hline $y$ & 7 & 4 & 1 & -2 & -5 \\ \end{tabular} \][/tex]

So the completed table is:

[tex]\[ \begin{tabular}{c|ccccc} $x$ & -4 & 0 & 4 & 8 & 12 \\ \hline $y$ & 7 & 4 & 1 & -2 & -5 \\ \end{tabular} \][/tex]