Proportionality

When 2 quantities are in direct proportion, as one increases so does the other or if one decreases so does the other

The general formula for this is:  y = kx

For example:

If y is directly proportional to x when x = 12 then y = 3. Find the constant of proportionality and the value of x when y = 8.

We know that y is proportional to x so y = kx

To find the value of k substitute the values y = 3 and x = 12 into y = kx

3 = k × 12

So k = 3/12 = 1/4

To find the value of x , when y = 8 substitute y = 8 and k = 1/4 into y = kx

8 = (1/4) x

So x = 32 when y = 8

Inverse proportion is when one value increases as the other decreases

The general formula for this is:  y ∝ ¹/_x

For example;

y is inversely proportional to x. When y = 3, x = 12 .Find the constant of proportionality, and the value of x when y =8.

y ∝ 1/x so y = k/x

xy = k  so substitute the values x = 12 and y = 3 into xy = k

3 × 12 = 36

Sok = 36

To find the value of x when y = 8, substitute k = 36 and y = 8 into xy = k

x = 36/8 = 4.5

QUADRATIC :  y ∝ x²

SQUARE ROOT:  y ∝

INVERSE PROPORTION:   y ∝ 1/x 

• Lines are asymptotes to the graph (they will never touch the axis)