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)
Comments
This information is so useful on March 03, 2013:
Thanx.............
Daria on January 16, 2012:
Information was very helpful
College-Student-Need-Help on January 11, 2012:
Thnx, this help[ed me very much :D
S on September 02, 2011:
Nice yr..............,:))
