Understanding formula / equation value changes

Consider the following equations:

• x + 5 = y
• 2x + 2 = y
• x - 10 = 4y
• x / 10 = y
• 10 - x = y
• 1 / x = y

This module is about understanding how a value of x varies with a value of y.

So for example, if x increases, does y increase as well or decrease?
- if y increase, does x then also increase or decrease?

These types of questions are coming up more in GCSE exams and besides this is a very worthwhile skill which will improve your overall ability in algebra.

The trick is to recognise the forms that result in direct or inverse proportion.

Direct: means if x increases, so does y, and vice-versa
Indirect: means if y increases, x decreases, and vice-versa.

The generic forms are as follows.

Direct proportion

• x = y
• x + number = y
• x - number = y
• x = y + number
• x = y - number
• x / number = y
• x = y / number

Indirect proportion

• -x = y
• x = -y
• number - x = y
• x = number - y
• number / x = y
• x = number / y

However, be aware that if two of the inverse forms are combined, they become direct:

Direct proportion ( via double indirect proportion )

• -x = 1 / y
• 1 / x = -y
• number - x = 1 / y
• 1 / x = number - y
• number / x = 1 / y
• 1 / x = number / y

In addition, bear in mind that multipliers , when positive, do not affect these rules.
If a multiplier is negative however, on one of the letters, then it will flip the result.

Examples:

x + 2 = y In this case, x will increase as y increases, and decrease as y decreases
x/2 + 2 = y also the same - as the divide-by-two is like a 0.5 x multiplier
3x + 2 = y also the same - the multiplier does not change the increase/decrease outcome
-3x + 2= y But here, the multiplier on x is negative, which leads to an inverse relationship:
                 As x increases, y decreases, and vice-versa.


Difficulty
The global difficulty level has no effect in this module.