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The graph shows a proportional relationship between \( x \) and \( y \), represented by a straight line passing through the origin. To determine the constant of proportionality, also called the slope, we need to calculate the ratio \( \frac{y}{x} \) using any clear point from the graph.

From the graph, one prominent point is \( (2, 4) \).

To find the constant of proportionality \( k \), we use the formula:
\[
k = \frac{y}{x}
\]
Substituting the values from the point \( (2, 4) \):
\[
k = \frac{4}{2} = 2
\]

Thus, the constant of proportionality is \( k = 2 \).

Would you like further explanation or have any questions?

Here are 5 related questions to further your understanding:
1. What is the significance of the constant of proportionality in a linear relationship?
2. How do you identify a proportional relationship on a graph?
3. How would the graph change if the constant of proportionality were 3 instead of 2?
4. Can a proportional relationship have a negative constant of proportionality? What would that look like on a graph?
5. How can you use the constant of proportionality to predict the value of \( y \) for any given \( x \)?

**Tip:** The constant of proportionality is the slope of the line, and it tells you how much \( y \) changes for every unit change in \( x \).

¿Cuál es la constante de proporcionalidad entre y y x en la gráfica?

Learn how to find the constant of proportionality from a graph where y is proportional to x. Using the point (2, 4) from the graph, calculate the constant of proportionality as k = 2. Suitable for students in Grades 6-8.

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