Question

This graph shows a proportional relationship.

What is the constant of proportionality?

Enter your answer as a decimal in the box.

Graph titled Change in Sea Level. The vertical axis is labeled amount of change in centimeters. The horizontal axis is labeled number of years. The horizontal x axis ranges from 0 to 24 in increments of 1 year. The vertical y axis ranges from 0 to 7 in increments of 0.5 centimeters. A line passes through the origin and the points begin ordered pair 5 comma 1.5 end ordered pair and begin ordered pair 20 comma 6 end ordered pair.

Answer 1

To find the constant of proportionality for a proportional relationship, we can use the formula:

\[ k = \frac{y}{x} \]

where \( k \) is the constant of proportionality, \( y \) is the value on the vertical axis, and \( x \) is the value on the horizontal axis.

From the points given on the graph:

1. Using the point (5, 1.5):
\[
k = \frac{1.5}{5} = 0.3
\]

2. Using the point (20, 6):
\[
k = \frac{6}{20} = 0.3
\]

In both cases, the constant of proportionality is the same.

Thus, the constant of proportionality is:

**0.3**