Let’s analyze the changes in the [tex]\( y \)[/tex] values for given [tex]\( x \)[/tex] values step by step.
Here are the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
1 & 4 \\
\hline
2 & 8 \\
\hline
3 & 12 \\
\hline
4 & 16 \\
\hline
5 & 20 \\
\hline
\end{tabular}
\][/tex]
First, let’s look at the changes in the values of [tex]\( y \)[/tex] as [tex]\( x \)[/tex] increases:
1. When [tex]\( x \)[/tex] changes from 1 to 2, [tex]\( y \)[/tex] changes from 4 to 8.
2. When [tex]\( x \)[/tex] changes from 2 to 3, [tex]\( y \)[/tex] changes from 8 to 12.
3. When [tex]\( x \)[/tex] changes from 3 to 4, [tex]\( y \)[/tex] changes from 12 to 16.
4. When [tex]\( x \)[/tex] changes from 4 to 5, [tex]\( y \)[/tex] changes from 16 to 20.
To determine the changes in [tex]\( y \)[/tex] values:
- For [tex]\( x \)[/tex] changing from 1 to 2, [tex]\( y \)[/tex] changes from 4 to 8, this difference is [tex]\( 8 - 4 = 4 \)[/tex].
- For [tex]\( x \)[/tex] changing from 2 to 3, [tex]\( y \)[/tex] changes from 8 to 12, this difference is [tex]\( 12 - 8 = 4 \)[/tex].
- For [tex]\( x \)[/tex] changing from 3 to 4, [tex]\( y \)[/tex] changes from 12 to 16, this difference is [tex]\( 16 - 12 = 4 \)[/tex].
- For [tex]\( x \)[/tex] changing from 4 to 5, [tex]\( y \)[/tex] changes from 16 to 20, this difference is [tex]\( 20 - 16 = 4 \)[/tex].
Since each interval shows a constant change of 4 in the [tex]\( y \)[/tex] value, we can conclude that the [tex]\( y \)[/tex] values are increasing by 4 each time.
Therefore, the statement that best describes how the [tex]\( y \)[/tex] values are changing over each interval is:
They are increasing by 4 each time.
