Key Points

Variation describes how two quantities are related, where a change in one quantity causes a corresponding change in another. This relationship can be a direct or inverse proportion.

Two quantities are in direct proportion if they increase or decrease together in such a way that the ratio of their corresponding values remains constant. For example, more articles purchased means a higher total cost.

If two quantities x and y are in direct proportion, their ratio is always a constant value, k. This is mathematically expressed as x/y = k.

To solve problems involving direct proportion, we use the formula x1/y1 = x2/y2, where (x1, y1) and (x2, y2) are two pairs of corresponding values.

To check if variables x and y in a table are directly proportional, calculate the ratio x/y for each column. If the ratio is the same for all pairs, they are in direct proportion.

Two quantities that increase or decrease together are not always in direct proportion. The key condition is that their ratio must be constant, which is not true for examples like age and height.

Two quantities are in inverse proportion if an increase in one quantity results in a proportional decrease in the other, and vice versa. For instance, increasing speed reduces the time taken to cover a fixed distance.

If two quantities x and y are in inverse proportion, their product is always a constant value, k. This is mathematically expressed as x * y = k.

To solve problems involving inverse proportion, we use the formula x1 * y1 = x2 * y2, where (x1, y1) and (x2, y2) are two pairs of corresponding values.

To check if variables x and y in a table are inversely proportional, calculate the product x * y for each column. If the product is the same for all pairs, they are in inverse proportion.

The number of workers on a job and the time taken to complete it are in inverse proportion. More workers will take less time to finish the same amount of work.

For a fixed distance, speed and time are in inverse proportion. For a fixed time, distance and speed are in direct proportion.