To find the constant of proportionality \( k \) for the points provided, we will use the coordinates of any of the points on the line. The points given are:
- \( (0, 0) \)
- \( (2, 14) \)
- \( (4, 28) \)
- \( (6, 42) \)
- \( (8, 56) \)
- \( (10, 70) \)
- \( (12, 84) \)
The constant of proportionality \( k \) can be determined by the formula:
\[ k = \frac{y}{x} \]
We can calculate \( k \) using one of the points (except for the origin):
Using the point \( (2, 14) \):
\[ k = \frac{14}{2} = 7 \]
To ensure consistency, we can check another point, for example, \( (4, 28) \):
\[ k = \frac{28}{4} = 7 \]
This calculation holds for all points listed since the ratio of \( y \) to \( x \) will be constant.
Thus, the constant of proportionality is:
\[ k = 7 \]