Direct Proportion
Direct proportion: As one variable (Y) increases ↑, another variable (X) increases↑ at the same proportion/rate.
=> as y increase ↑, x also increases ↑ proportionally
y α x Symbol of proportion: α
The equation for direct proportion is
y = kx (where k is the constant of proportionality)
Example y is proportional to x and y = 20 when x = 25. Find y when x = 10.
Step 1: Write out the Formula
y α x
Step 2: Find k (the constant)
y = kx
20 = k x 25
k = 20 / 25 = 4/5
Step 3: Solve
y = 4/5 x
When x = 10,
y = 4/5 x 10
= 8
Inversely Proportion
Inversely: As one variable (Y) increases↑, another variable (X) decreases ↓ at the same proportion/rate.
=> As y increases ↑, x decreases ↓ proportionally
The equation for inverse proportion:
y= k
x (where k is the constant of proportionality)
Example:
y is inversely proportional to x and y = 20 when x = 25. Find y when x = 10.
Step 1: Write the formula
y α 1/x
y = k/x
Step 2: Find k (the constant)
20 = k/25
k = 20 x 25
= 500
Step 3: Solve
y = 500/x
When x = 10,
y = 500/10 = 50
Practice
1. A swimming pool can be filled with water in 12 hours using 4 pumps. How many hours would it take if 8 pumps were used? [17/II/4/2/T]
2. Team A have won 14 of their 20 matches. Team B have won 2/3 of their matches. Which team have won the greater proportion of their matches [16/II/7/3/T]
3. The time taken to build a wall is inversely proportional to the number of people building it. 8 people can build the wall in 15 days.
How long will it take 12 people to build it? [11/II/17a/2/A]
4. Y is directly proportional to x3. When x has a certain value, y = 5. Find the value of y when x is doubled. [11/I/21b/2/A]
5. S is directly proportional to t2. Given that s = 27 when t = 9, find
a. an expression fro s in terms of t.
b. the value of t when s = 1/12 [13/I/14/3/A]
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