The table below shows a relationship between *x* and *y*.

*x y*

0

0

3

24

7

56

11

88

15

120

What is the constant of proportionality

To determine the constant of proportionality between \( x \) and \( y \), we need to check if the relationship between \( x \) and \( y \) is proportional. A proportional relationship is one in which \( y \) is directly proportional to \( x \), meaning the ratio \( \frac{y}{x} \) is constant.

Let's calculate the ratio \( \frac{y}{x} \) for each pair of values in the table:

1. For \( x = 3 \) and \( y = 24 \):
   \[
   \frac{y}{x} = \frac{24}{3} = 8
   \]

2. For \( x = 7 \) and \( y = 56 \):
   \[
   \frac{y}{x} = \frac{56}{7} = 8
   \]

3. For \( x = 11 \) and \( y = 88 \):
   \[
   \frac{y}{x} = \frac{88}{11} = 8
   \]

4. For \( x = 15 \) and \( y = 120 \):
   \[
   \frac{y}{x} = \frac{120}{15} = 8
   \]

Since the ratio \( \frac{y}{x} \) is constant and equal to 8 for all values of \( x \), the constant of proportionality is **8**.

Would you like more details on how this works or have any questions?

Here are 5 related questions:
1. How can you use the constant of proportionality to predict \( y \) for any given \( x \)?
2. How does the concept of proportionality relate to linear equations?
3. What happens if the relationship between \( x \) and \( y \) is not proportional?
4. Can you have a proportional relationship if one of the values of \( x \) is 0?
5. How do you determine proportionality from a graph?

**Tip**: In a proportional relationship, the graph of \( y \) vs. \( x \) will always be a straight line passing through the origin.

The table below shows a relationship between *x* and *y*. 

*x  y*

0  0

3  24

7  56

11 88

15 120

What is the constant of proportionality?

Learn how to determine the constant of proportionality from a table of values showing a relationship between x and y. This step-by-step solution covers key concepts in ratios and direct proportionality. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation