# Opinions on **Proportionality (mathematics)**

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In mathematics, two variables are **proportional** if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant multiplier. The constant is called the coefficient of proportionality or **proportionality constant**.

- If one variable is always the product of the other and a constant, the two are said to be
*directly proportional*.*x*and*y*are directly proportional if the ratio is constant. - If the product of the two variables is always equal to a constant, the two are said to be
*inversely proportional*.*x*and*y*are inversely proportional if the product is constant.

To express the statement, "y is proportional to x," we write as an equation y = cx, for some real constant c. Symbolically, we write y ∝ x.

To express the statement, "y is inversely proportional to x," we write as an equation y = c/x. We can equivalently write, "y is proportional to 1/x", which y = c/x would represent.

If a linear function transforms 0, *a* and *b* into 0, *c* and *d*, and if the product *a b c d* is not zero, we say *a* and *b* are proportional to *c* and *d.* An equality of two ratios such as where no term is zero, is called a proportion.

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