To determine the slope of the line using the points provided, we first need to choose two points. The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's select the points (0, 0) and (8, 4).
Here:
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (8, 4) \)
Now, substituting these values into the slope formula:
\[ m = \frac{4 - 0}{8 - 0} = \frac{4}{8} = \frac{1}{2} \]
We can verify this by using any other pair of points from the list. Let's check using the points (2, 1) and (8, 4):
Here:
- \( (x_1, y_1) = (2, 1) \)
- \( (x_2, y_2) = (8, 4) \)
Now substituting these values into the slope formula:
\[ m = \frac{4 - 1}{8 - 2} = \frac{3}{6} = \frac{1}{2} \]
If we choose another pair (6, 3) and (0, 0):
\[ m = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \]
All pairs yield a consistent slope. Hence, the slope of the line is:
\[ \text{slope} = \frac{1}{2} \]