VARIATIONS

CONTENT

1. Direct Variation
2. Inverse Variation
3. Joint Variation
4. Partial Variation

Direct Variation

A football club gives a cash bonus ₦5,000 for each goal scored by the players.

The table below shows the relationship between the number of goals scored and the cash bonuses.

Table

Observe that the more goals scored, the greater the cash bonus received.

We say that \(y\) varies directly as \(x\).

The symbol of variation is \(\text{ ∝ }\)

Thus \(y\) varies directly as can be written in symbolic form as \(y \text{ ∝ } x\).

Thus if \(y \text{ ∝ } x\), then \(y = kx\)

Where \(k\) is called a constant of variation.

In this particular case; \(k = 5000\)

Examples:

1. If \(y\) varies directly as \(x\), write down the equation connecting \(y\) and \(x\). For \(y = 10\), and \(x = 5\), find the value of the constant, hence calculate the value of \(y\) when \(x = 16\).

Solution:

\(y \text{ ∝ }x\) (direct variation)

\(y = kx\) (k, constant of variation)

Substitute \(y = 10, x = 5\) in the equation \(y = kx\) to obtain \(10 = 5k\).