Question

This graph shows a proportional relationship.

What is the constant of proportionality?

Enter your answer in the box.

Graph titled Math Test Raw Scores. The vertical axis is labeled Points. The horizontal axis is labeled Correct answers. The horizontal axis ranges from 0 to 24 in increments of 2. The vertical axis ranges from 0 to 120 in increments of 10. A line passes through the origin and the points begin ordered pair 5 comma 30 end ordered pair and begin ordered pair 12 comma 72 end ordered pair and begin ordered pair 18 comma 108 end ordered pair and begin ordered pair 20 comma 120 end ordered pair.

Answer 1

To determine the constant of proportionality from the graph you've described, we can use any of the points given. The constant of proportionality \( k \) is defined as the ratio of the output (Points) to the input (Correct answers).

Taking the point (5, 30) as an example, we can calculate \( k \) as follows:

\[
k = \frac{\text{Points}}{\text{Correct answers}} = \frac{30}{5} = 6
\]

We can verify this with another point, for example (12, 72):

\[
k = \frac{72}{12} = 6
\]

And checking with (18, 108):

\[
k = \frac{108}{18} = 6
\]

Finally, checking (20, 120):

\[
k = \frac{120}{20} = 6
\]

Since all calculations give the same result, the constant of proportionality is:

\[
\boxed{6}
\]