Question

What is constant of proportionality, definition, example

Answer 1

The constant of proportionality is a value that relates two proportional quantities. In other words, it is the ratio between two variables that are directly proportional to one another. If two quantities, \( y \) and \( x \), are directly proportional, we can write this relationship as:

\[ y = k \cdot x \]

where \( k \) is the constant of proportionality. This means that for any value of \( x \), the value of \( y \) can be found by multiplying \( x \) by \( k \).

### Definition:
The constant of proportionality is a specific constant value that defines the relationship between two variables that are in direct proportion to each other. It is often denoted as \( k \) and is a dimensionless number in many applications.

### Example:
Consider a scenario where a car travels at a constant speed of 60 miles per hour. The distance \( d \) traveled by the car is directly proportional to the time \( t \) taken, such that:

\[ d = k \cdot t \]

In this case, the constant of proportionality \( k \) is 60 (miles per hour). This means:

- If the car travels for 1 hour, then \( d = 60 \times 1 = 60 \) miles.
- If the car travels for 2 hours, then \( d = 60 \times 2 = 120 \) miles.
- If it travels for 3 hours, \( d = 60 \times 3 = 180 \) miles.

In this example, the ratio of distance to time remains constant at 60, which indicates the speed of the car.