To determine the direction of the trend line for the given data, we need to understand the relationship between the x-values (2, 4, 5, 6, 7, 10) and the y-values (0, 1, 2, 5, 6, 10). The trend line in question is described by the equation of a linear regression line, which is of the form:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\(m\)[/tex] represents the slope and [tex]\(b\)[/tex] represents the y-intercept.
### Slope
The slope ([tex]\(m\)[/tex]) indicates the steepness and the direction of the trend line:
- A positive slope indicates an increasing trend line.
- A negative slope indicates a decreasing trend line.
- A zero slope indicates a horizontal trend line.
For the given data, after performing a linear regression analysis, we obtain:
[tex]\[ m = 1.3392857142857142 \][/tex]
[tex]\[ b = -3.5892857142857064 \][/tex]
The key component here is the slope [tex]\(m\)[/tex]. Let's examine its value:
### Analysis
The slope [tex]\(m = 1.3392857142857142\)[/tex] is positive. A positive slope means that as the x-values increase, the y-values also increase. This results in a trend line that slopes upwards from left to right.
### Conclusion
Since the slope is positive, the trend line will be increasing when we plot the data.
So, the correct answer to the question is:
Increasing
