5.3. Variation

Question 1

Directly proportional

Answer 1

x ∝ y

X varies as y
X varies directly as y
X is proportional to y

The numbers have a ‘constant ratio’

Question 2

Solving ‘k’ in direct proportionality

x ∝ y

If x = 3 and y = 12

Answer 2

x ∝ y → x = ky

If x = 3 and y = 12

3 = k*12

k = ¼

Replace k with ¼

x = ¼ y

(This is the equation describing the ratio between these two values, regardless of what size they are)

Question 3

Inverse proportionality

Answer 3

x ∝ 1/y

x varies inversely as y
x is inversely proportional to y

As one quantity increases, the other decreases constantly

Question 4

Solving ‘k’ in inverse proportionality

x ∝ 1/y

x = 120 when y = 5.

Answer 4

x ∝ 1/y –> x = k/y

120 = k/5

k = 600

x ∝ 600/y