\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
1000 & 20 \\
\hline
1000 & 23 \\
\hline
1000 & 26 \\
\hline
1000 & 29 \\
\hline
1000 & 32 \\
\hline
\end{tabular}

What can you conclude about the slope of the values in the table? Check all that apply.

A. The slope is 3.
B. The slope is 0.
C. The slope is undefined.
D. The graph will be a horizontal line.
E. The graph will be a vertical line.
F. The graph will have a line with a positive slope.



Answer :

To determine the slope of the values in the table, let's go through the steps required for calculating the slope:

1. Identify the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values from the table:
- [tex]\(x\)[/tex] values: 1000, 1000, 1000, 1000, 1000
- [tex]\(y\)[/tex] values: 20, 23, 26, 29, 32

2. The slope ([tex]\(m\)[/tex]) can be calculated using the formula [tex]\( m = \frac{\Delta y}{\Delta x} \)[/tex]:
- [tex]\(\Delta y\)[/tex] is the change in [tex]\(y\)[/tex] values.
- [tex]\(\Delta x\)[/tex] is the change in [tex]\(x\)[/tex] values.

3. Calculate [tex]\(\Delta y\)[/tex]:
- [tex]\(\Delta y = y_{\text{last}} - y_{\text{first}} = 32 - 20 = 12\)[/tex]

4. Calculate [tex]\(\Delta x\)[/tex]:
- [tex]\(\Delta x = x_{\text{last}} - x_{\text{first}} = 1000 - 1000 = 0\)[/tex]

5. Since [tex]\(\Delta x = 0\)[/tex], we cannot divide by zero, indicating that the slope is undefined (or considered as [tex]\( \infty \)[/tex]).

From this calculation, we can make the following conclusions about the slope and the graph of the values in the table:

- The slope is undefined. This is because [tex]\(\Delta x = 0\)[/tex] makes the slope calculation undefined.
- The graph will be a vertical line. Since all [tex]\(x\)[/tex] values are the same (1000), the graph forms a vertical line parallel to the [tex]\(y\)[/tex]-axis.

Therefore, the correct statements are:
- The slope is undefined.
- The graph will be a vertical line.