91Ó°ÊÓ

Direct Variation: Two variables \(x\) and \(y\) have a direct relationship if their ratio is constant. This means that if \(x\) increases, \(y\) will also increase and vice versa. In terms of mathematical formula, it can be expressed as \(y = kx\), where \(k\) is the constant of variation. \n\n Inverse Variation: Two variables \(x\) and \(y\) have an inverse relationship if their product is constant. This means that if \(x\) increases, \(y\) will decrease and vice versa. In terms of mathematical formula, it can be expressed as \(xy = k\), where \(k\) is the constant of variation. \n\n Joint Variation: A variable \(y\) varies jointly with variables \(x\) and \(z\) if \(y\) is directly proportional to the product of \(x\) and \(z\). The formula for joint variation is \(y = kxz\), where \(k\) is the constant of variation.

Read the problem carefully. The problem itself will usually specify if it’s a 'direct variation' by using terms like 'is proportional to' or if it’s an 'inverse variation' by using terms like 'varies inversely'. If it states that one quantity varies directly as the product of two or more others, then it is a 'joint variation'.

Using what identify from the problem statement, formulate an equation reflecting the type of variation specified. If it is a direct variation, use the formula \(y = kx\). If it is an inverse variation, use the formula \(xy = k\). If it is a joint variation, use the formula \(y = kxz\). In these formulas, \(k\) is the constant which can be calculated using given values.

Solve the equation formulated in the previous step. The solving method may vary depending on the complexity of the equation and the values given in the problem. This, however, usually involves simple algebraic manipulation, where you'll rearrange to make the unknown subject of the formula and substitute given values in order to find it.