Let's work through the problem step by step, filling in the table.
We are given the equation [tex]\(y = 12x - 4\)[/tex] which represents Francisco's earnings [tex]\(y\)[/tex] after transportation costs for working [tex]\(x\)[/tex] hours. To create the table, we will substitute the values of [tex]\(x\)[/tex] into this equation to find the corresponding [tex]\(y\)[/tex] values.
Let's start with [tex]\(x = 1, 2, 3,\)[/tex] and [tex]\(4\)[/tex]:
1. For [tex]\(x = 1\)[/tex]:
[tex]\[
y = 12(1) - 4 = 12 - 4 = 8
\][/tex]
2. For [tex]\(x = 2\)[/tex]:
[tex]\[
y = 12(2) - 4 = 24 - 4 = 20
\][/tex]
3. For [tex]\(x = 3\)[/tex]:
[tex]\[
y = 12(3) - 4 = 36 - 4 = 32
\][/tex]
4. For [tex]\(x = 4\)[/tex]:
[tex]\[
y = 12(4) - 4 = 48 - 4 = 44
\][/tex]
Now, we can fill in the table with those values:
\begin{tabular}{|l|l|l|l|l|}
\hline
[tex]$x$[/tex] (number of hours) & 1 & 2 & 3 & 4 \\
\hline
[tex]$y$[/tex] (earnings in dollars) & 8 & 20 & 32 & 44 \\
\hline
\end{tabular}
