Let's fill in the [tex]\( t \)[/tex]-table for the equation [tex]\( y = 3x + 4 \)[/tex].
First, we will find the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value.
1. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 3(-1) + 4 = -3 + 4 = 1
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 3(0) + 4 = 0 + 4 = 4
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = 4 \)[/tex].
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 3(1) + 4 = 3 + 4 = 7
\][/tex]
So, when [tex]\( x = 1 \)[/tex], [tex]\( y = 7 \)[/tex].
Now, let's fill in the [tex]\( t \)[/tex]-table with these values:
[tex]\[
\begin{tabular}{|r|r|}
\hline
$x$ & $y$ \\
\hline
-1 & 1 \\
\hline
0 & 4 \\
\hline
1 & 7 \\
\hline
\end{tabular}
\][/tex]
To select two points from the table, we can choose any two. Here are two examples:
1. [tex]\((-1, 1)\)[/tex]
2. [tex]\((0, 4)\)[/tex]
These points represent solutions to the equation [tex]\( y = 3x + 4 \)[/tex].
