Calculate Direct Proportion Using Formal Notation

In this activity, we will use direct proportion to find a formula connecting two unknowns.

Recap

We have seen this before when we are creating coordinates to draw graphs.

For example y = 2x

We follow the rule of y = 2 multiplied by the x value:

The graph can now be plotted!

We are using the same idea for this activity!

From the recap above:

y is directly proportional to x

In fact, as x goes up, y goes up by double because we are multiplying x by 2

Let's try a typical question!

Example

A is directly proportional to B

When A = 8, B = 2

Find a formula for A in terms of B.

Answer

We write A is directly proportional to B like this:

The letter in the middle is the Greek letter alpha and it means 'proportional to' here.

Now, we know they both go up proportionally, but we do not know the multiplier (or exchange rate if it was currency exchange).

So, we write

A = KB

Where K is just a letter used for the multiplier because we are unsure what it is at the minute.

To find K (the multiplier) we use the values given in the question.

A = 8 when B = 2

Substitute in

A = KB

8 = 2K

Divide through by 2

K = 8 ÷ 2

K = 4

We can now write the formula as we know the multiplier K

A = 4B

Now we can use this to find any missing value of A or B

Confused? 

We will do the first question together to help! It gets easier quickly!