To determine the slope of the line using similar triangles, we can look at the given points and recognize that they create a straight line.
The formula for the slope \( m \) of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the first two points (0, 0) and (2, 1) to calculate the slope:
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 1) \)
Substituting these values into the formula gives us:
\[ m = \frac{1 - 0}{2 - 0} = \frac{1}{2} \]
Now, let's confirm that the slope remains the same as we use other pairs of points.
Using the second and third points (2, 1) and (4, 2):
- \( (x_1, y_1) = (2, 1) \)
- \( (x_2, y_2) = (4, 2) \)
Substituting these values gives:
\[ m = \frac{2 - 1}{4 - 2} = \frac{1}{2} \]
Using the third and fourth points (4, 2) and (6, 3):
- \( (x_1, y_1) = (4, 2) \)
- \( (x_2, y_2) = (6, 3) \)
Substituting these gives:
\[ m = \frac{3 - 2}{6 - 4} = \frac{1}{2} \]
Using the fourth and fifth points (6, 3) and (8, 4):
- \( (x_1, y_1) = (6, 3) \)
- \( (x_2, y_2) = (8, 4) \)
Substituting gives:
\[ m = \frac{4 - 3}{8 - 6} = \frac{1}{2} \]
All calculations yield the same slope, confirming that the slope of the line is:
\[ \boxed{\frac{1}{2}} \]