Variation

Direct Variation

 

Direct variation always has the following formula.

 

Y = mx

 

Direct variation is always a straight line and must start at the coordinate (0,0)

 

Example:

 

A cyclist is riding at 10km/h

 

a)    What distance has the cyclist travelled in 3 hours

- 30km

b)   What distance has the cyclist travelled in 6 hours

- 60km

 

We can say that distance varies directly with time. If you double the time, you double the distance.

 

This problem can be represented as: d = 10t where d represents distance and t represents time.

 

Partial Variation

 

Partial variation always has the following formula.

 

Y = mx + b

 

Partial variation is always a straight line; it does not need to start at (0,0)

 

Example:

 

Alice is paid $8/hour + $20 flat rate.

 

The equation would be: p = 8h+20

Where p is the pay, and h is the number of hours.

 

See the Chapter 5 notes here fore more notes about direct and partial variation!