Direct and inverse proportion

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 mathematically 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 mathematically as y = k/x, where k is a constant.

Front

How do you identify a direct proportion equation?

Back

A direct proportion equation can be identified by the form y = kx, where k is a non-zero constant. The graph of this relationship is a straight line that passes through the origin.

Front

How do you identify an inverse proportion equation?

Back

An inverse proportion equation can be identified by the form y = k/x, where k is a non-zero constant. The graph of this relationship is a hyperbola.

Front

If y varies directly as x and y = 10 when x = 5, what is the value of y when x = 10?

Back

y = 20. Since y varies directly as x, if x doubles, y also doubles.

Front

If 8 workers can complete a task in 12 days, how long will it take 4 workers to complete the same task?

Back

24 days. This is an example of inverse proportion, where the number of workers and the time taken are inversely related.

Front

What is the formula to calculate the constant of variation in direct proportion?

Back

The constant of variation (k) in direct proportion can be calculated using the formula k = y/x.

Front

What is the formula to calculate the constant of variation in inverse proportion?

Back

The constant of variation (k) in inverse proportion can be calculated using the formula k = xy.

Front

In a direct proportion, if x = 4 and y = 8, what is the constant of proportionality?

Back

The constant of proportionality (k) is 2, since k = y/x = 8/4.

Front

In an inverse proportion, if x = 3 and y = 12, what is the constant of proportionality?

Back

The constant of proportionality (k) is 36, since k = xy = 3 * 12.