Variation Flashcards
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
- Look at the question to see what value of ‘x’ y is directionally proportional to.
y α x
- Replace the α with ‘=k’ (the constant of proportionality).
y = kx
- Find ‘k’
10 = k x 4
k = 10/4 = 5/2
- Write the equation, replacing ‘k’ with its found value.
y = 5/2 x
- 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
What does inverse proportion mean?
As one thing increases (eg. Number of people), another decreases (eg. Amount of cake)
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
- Look at the question to see what value of x y is inversely proportional to.
y α x
- Replace the α with ‘=k’ (the constant of proportionality).
y = k/x
- Find ‘k’
6 = k/20
k = 120
- Write the equation, replacing ‘k’ with its found value (this is answer to part a)).
y = 120/x
- Apply the equation
b) y = 120/40 = 3
c) 2 = 120/x
2x = 120
x = 60
Is y α x2 directly or inversely proportional?
Directly
Is y α square root of x directly or inversely proportional?
Directly
Is y α x3 directly or inversely proportional?
Directly
Is y α 2/x directly or inversely proportional?
Inversely
Is y α x directly or inversely proportional?
Directly
Is y α 2/x2 directly or inversely proportional?
Inversely
