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.
