Lesson plan

Proportion

We admit that  is equivalent to each of the following: 

In a particular case  is equivalent to  or

Definition:

Two numbers are respectively proportional to the non zero numbers m and n if and only if  .

Example: Determine three numbers x, y and z respectively proportional to 2, 3 and 4 such that:  .

Solution: We have the following system:  

where k is a constant to be determined.

we can conclude that x = 2k , y = 3k, z = 4k.

Substitute the values of x, y and z in the equation            

   ;           ;    

Replace  by its value; we obtain:

Proportion and algebraic relation:

Two quantities are proportional if one of them is a linear function of the other. In other term, if  (linear function or algebraic expression) where a is called the rate of the Proportion or the coefficient of proportionality.

Example:

	2	5	1	7
	12	30	6	42

Verify that the given table is a proportionality table; find its rate and determine its algebraic expression.

Solution:

So This table is a proportionality table.

The rate:

The linear function:  ;    .

Graphic representation:

The graph of a linear function of proportionality is a straight line passing through the origin of coordinates.

Consider the preceding example  . To construct this line we choose two values of x and calculate the corresponding y:

x	0	1
y	0	6