Variation

Question 1

How does one calculate x or y when y is directly proportional to x?

eg. Two quantities x are such that y α x

when x = 4, y = 10

a) Find y when x = 6
b) Find x when y = 8

Answer 1

1. Look at the question to see what value of ‘x’ y is directionally proportional to.

y α x

2. Replace the α with ‘=k’ (the constant of proportionality).

y = kx

3. Find ‘k’

10 = k x 4

k = 10/4 = 5/2

4. Write the equation, replacing ‘k’ with its found value.

y = 5/2 x

5. Apply the equation

a) y = 5/2 x 6 = 15

b) 8 = 5/2 x x

x = 8 ≈ 5/2 = 8/1 x 2/5 = 16/5 = 3.2

Question 2

What does inverse proportion mean?

Answer 2

As one thing increases (eg. Number of people), another decreases (eg. Amount of cake)

Question 3

How does one calculate x or y when y is inversely proportional to x?

eg. Two quantities x and y are such that y is inversely proportional to x

when x = 20, y = 6

a) Find a formula linking x and y
b) Find y when x = 40
c) Find x when y = 2

Answer 3

1. Look at the question to see what value of x y is inversely proportional to.

y α x

2. Replace the α with ‘=k’ (the constant of proportionality).

y = k/x

3. Find ‘k’

6 = k/20

k = 120

4. Write the equation, replacing ‘k’ with its found value (this is answer to part a)).

y = 120/x

5. Apply the equation
   b) y = 120/40 = 3
   c) 2 = 120/x

2x = 120

x = 60

Question 4

Is y α x² directly or inversely proportional?

Answer 4

Directly

Question 5

Is y α square root of x directly or inversely proportional?

Answer 5

Directly

Question 6

Is y α x³ directly or inversely proportional?

Answer 6

Directly

Question 7

Is y α 2/x directly or inversely proportional?

Answer 7

Inversely

Question 8

Is y α x directly or inversely proportional?

Answer 8

Directly

Question 9

Is y α 2/x² directly or inversely proportional?

Answer 9

Inversely