Direct and Inverse Proportions

Front

What is direct proportion?

Back

Direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable. It can be expressed as y = kx, where k is a constant.

Front

What is inverse proportion?

Back

Inverse proportion is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable. It can be expressed as xy = k, where k is a constant.

Front

If q is inversely proportional to p^2, what is the general form of the equation connecting p and q?

Back

The general form is q = k/p^2, where k is a constant.

Front

How do you determine the constant of variation in inverse proportion?

Back

To determine the constant of variation, multiply the two variables together (xy = k) using known values.

Front

What happens to the time taken to complete a job if the number of workers increases?

Back

The time taken to complete the job decreases, indicating an inverse proportion between the number of workers and the time taken.

Front

What is the relationship between population density and area in a fixed space?

Back

As the population increases in a fixed area, the area available per person decreases, demonstrating inverse variation.

Front

How can you express a problem involving direct proportion mathematically?

Back

A problem involving direct proportion can be expressed as y = kx, where y and x are the variables and k is the constant of proportionality.

Front

What is the formula for calculating the time taken when the number of workers changes in a construction problem?

Back

If W1 is the initial number of workers, T1 is the initial time, W2 is the new number of workers, and T2 is the new time, the relationship can be expressed as W1 * T1 = W2 * T2.

Front

What is an example of a direct proportion in real life?

Back

An example of direct proportion is the relationship between distance and time when traveling at a constant speed.

Front

What is an example of an inverse proportion in real life?

Back

An example of inverse proportion is the relationship between the number of workers and the time taken to complete a task; as the number of workers increases, the time taken decreases.