Final answer:
The constant of proportionality for the line can be found by calculating the slope using two points on the line, which is done by dividing the change in y by the change in x. Using the points (6.4 s, 2000 m) and (0.50 s, 525 m), the constant of proportionality is found to be 250 m/s.
Step-by-step explanation:
To find the constant of proportionality for a line representing a proportional relationship, you would typically use two points on the line to calculate the slope. In this case, we are provided with two points on the line: (6.4 s, 2000 m) and (0.50 s, 525 m). To calculate the slope, also known as the rate of change or the proportionality constant, we follow these steps:
Subtract the y-coordinate of the second point from the y-coordinate of the first point to get the change in y. (2000 m - 525 m = 1475 m)
- Subtract the x-coordinate of the second point from the x-coordinate of the first point to get the change in x. (6.4 s - 0.50 s = 5.9 s)
- Divide the change in y by the change in x to get the slope. (1475 m / 5.9 s = 250 m/s)
Therefore, the constant of proportionality for this line is 250 m/s. This means for every second, the quantity increases by 250 meters. In this context, the constant represents a speed, showing how many meters are traveled each second if the relationship described by the line continues to hold.