The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 450 and 8 comma 600.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
To find the constant of proportionality, we need to calculate the ratio between the change in the number of gems collected and the change in the number of levels completed.
First, we calculate the change in the number of gems collected: 600 - 450 = 150.
Next, we calculate the change in the number of levels completed: 8 - 6 = 2.
The constant of proportionality is then given by the ratio of these two changes: 150/2 = 75.
Therefore, the correct answer is p = 75.
To determine the constant of proportionality for the relationship, we need to find the ratio between the change in the number of gems collected and the corresponding change in the number of levels completed.
We can do this by selecting any two points on the line and calculating the ratio.
Let's choose the points (6, 450) and (8, 600).
The change in the number of gems collected is 600 - 450 = 150.
The corresponding change in the number of levels completed is 8 - 6 = 2.
Therefore, the constant of proportionality, or the ratio, is:
p = 150 / 2 = 75.
So, the correct answer is p = 75.
To determine the constant of proportionality for the relationship between the number of gems collected and the number of levels completed, we can use the formula:
Constant of Proportionality (p) = Change in y / Change in x
In this case, the "Change in y" represents the change in the number of gems collected, and the "Change in x" represents the change in the number of levels completed.
Let's calculate the changes:
Change in y = 600 - 450 = 150
Change in x = 8 - 6 = 2
Now, we can substitute these values into the formula:
p = Change in y / Change in x = 150 / 2
Calculating the value:
p = 75
Therefore, the constant of proportionality for the relationship is 75.