Deriving Equations

## Deriving Equations

Equations can be derived :

• when the value of one item varies with another;

• there is a rate (often seen with the word per) that multiplies the item;

• a starting value, which is added (or subtracted).

If the change is linear (a straight line), the data items can be laid out as an equation:

result = rate x item + starting value

which corresponds to

y=mx+c

## Example 1

A taxi firm charges £2.85 per kilometre, plus a £2 hire charge. If my taxi fare was £17.96, what distance did I travel?

The equation is: text(cost) = 2.85 xx text(distance) + 2

 Rewrite as c = 2.85d + 2 Substituting 17.96 = 2.85d + 2 Subtract 2 from both sides 15.96 = 2.85d   Divide both sides by 2.85 5.6 = d  

 Create an equation shift = rate x parts + warmup replace with letters s = rp + w Substitute, using minutes 8xx60 = 5xx92 + w calculate 480 = 460 + w Subtract 460 from both sides 20 =   w