Direct and inverse proportion examples with graphs (inversely and directly proportional formulas)

In this hub I will explain the difference between inverse proportion and direct proportion.

If m is directly proportional to n then the formula is:

m = kn

If m is inversely proportional to n then the formula is:

m = k/n

k is known as the constant of proportionality. Notice with direct proportion you multiply k by n and direct proportion k is being divided by n.

Let’s take a look at an example:

a) If y is directly proportional to x, and when x = 6 y = 3, find a formula connecting y and x.

b) This time y is inversely proportional to x, find a formula for y using the same boundary conditions as part a).

Answers

a) Since y is directly proportional to x then the formula is going to be y = kx.

The next thing you need to do is sub in the values x = 6 and y = 3 into this formula to calculate the constant of proportionality:

3 = k × 6

So to find k, all you need to do is divide the left hand side of the equation by 6:

3/6 = k

0.5 = k

Since k has now been found, you can plug this back into the formula that you started off with:

y = 0.5x

b) This time y is inversely proportional to x then the formula is going to be y = k/x.

Like part a), the next thing you need to do is sub in the values x = 6 and y = 3 into this formula to calculate the constant of proportionality:

3 = k ÷ 6

So to find k, all you need to do is multiply the left hand side of the equation by 6:

3 × 6 = k

18 = k

Since k has now been found, you can plug this back into the formula that you started off with:

y = 18/x

If you plot these two formulas on a graph you will notice that part a is an increasing formula and part b is a decreasing formula as x increases.

For some more help on direct and inverse proportion check out these hubs:

Direct proportion. How to write down a formula if y is directly proportional to x. Maths GCSE.

Inverse proportion word problems with graphs ( the meaning of y is inversely proportional to x)

More by this Author


Comments 4 comments

This information is so useful 3 years ago

Thanx.............


Daria 4 years ago

Information was very helpful


College-Student-Need-Help 4 years ago

Thnx, this help[ed me very much :D


5 years ago

Nice yr..............,:))

    0 of 8192 characters used
    Post Comment

    No HTML is allowed in comments, but URLs will be hyperlinked. Comments are not for promoting your articles or other sites.


    Click to Rate This Article
    working