# Define the term inverse proportionality? Then differentiate between direct and Inverse proportionality. ?

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• A dependent variable is inversely proportional when its value increases linearly with a decreasing value of the independent variable or decreases linearly with an increasing value of the independent variable.

A dependent variable is directly proportional when its value increases linearly with an increasing value of the independent variable or decreases linearly with a decreasing value of the independent variable.

EX:  When y = k/x it is inversely proportional to x as when x gets smaller y gets bigger and vice versa.  But when y = kx it is directly proportional to x as when x gets smaller y gets smaller and vice versa.

• It's pretty simple.

If two terms are directly proportional, then as one goes up, the other also goes up by some constant factor.

A common example is wages. If you are paid \$10 an hour, then as you work more hours, your wage goes up. Wages and hours are *directly* proportional.

If two terms are inversely proportional, then as one goes up, the other goes down.

A common example is speed and time. For example, if you drive to work (30 miles away) at a slower speed it takes *more* time. But if you drive to work at a faster speed, it takes *less* time. Speed and time are *inversely* proportional

In the first case, you can model that as a constant *times* the second variable.

Wages = Fixed hourly rate * hours

w = 10 * h

In the second case, you can model that as a constant *divided* by the second variable.

Time = Fixed distance / Speed

t = 30 / s

In general, if we say y is *directly* proportional to x, you'd write:

y = kx

If you say y is *inversely* proportional to x, you'd write:

y = k/x

In both cases, k is the constant of proportionality. The only difference is you multiply by x in the direct case and you divide by x in the inverse case.

• Anonymous
3 months ago

Is there any reason you don't award a Best Answer?  E.g. https://au.answers.yahoo.com/question/index?qid=20...

• Given 2 variables x and y, x has INVERSE PROPORTIONALITY to y if

.................1

..........y = --- x

.................k

where k is some constant.

Similarly, x has DIRECT PROPORTIONALITY to y if

..........y = k x

where k is some constant.

Example of DIRECT PROPORTIONALITY: The more money you have, the more food you can buy.

Example of INVERSE PROPORTIONALITY. The more money you spend, the less savings you have.