Lines a, b, and c on the graph represent proportional relationships. The constant of proportionality for each line can be determined by the ratio of the y-value to the x-value for any point on that line.
1. For line a (red line):
- The line goes through points like (1, 9) and (2, 8).
- The constant of proportionality can be determined from one of these points, say (1,9). It is
= 9.
2. For line b (purple line):
- This line goes through points such as (1, 10) and (2, 8).
- The slope or rate of change (rise over run) is not consistent between these points, meaning it's not a strict proportional relationship based on the given points. However, if we assume it's proportional and take point (1,10), the constant would be
= 10. But remember, it's not consistently proportional based on the two points provided.
3. For line c (black line):
- The line goes through the origin (0,0) and point (1, 3).
- Thus, the constant of proportionality is
= 3.
In summary:
- Line a: Constant of proportionality = 9
- Line b: The line does not represent a consistent proportional relationship based on the two points provided, but if we had to choose a value, it would be 10 based on point (1,10).
- Line c: Constant of proportionality = 3.