Two quantities are in direct proportion if they increase or decrease at the same rate
What is the formula for direct proportion?
y = kx
Match the variable with its meaning in the direct proportion formula:
y ↔️ Dependent variable
x ↔️ Independent variable
k ↔️ Constant of proportionality
If the cost of pencils is directly proportional to the number purchased, and each pencil costs £0.50, then k = 0.50
If the cost of 3 pencils is £1.50, what is the cost of 5 pencils according to direct proportion?
£2.50
Two quantities are in inverse proportion if their product remains constant.
What is the formula for inverse proportion?
y = k/x
Match the variable with its meaning in the inverse proportion formula:
y ↔️ Dependent variable
x ↔️ Independent variable
k ↔️ Constant of proportionality
If the time taken to paint a wall is inversely proportional to the number of painters, then the constant of proportionality (k) is the time taken by one painter.
If one painter takes 6 hours to paint a wall, how long will 2 painters take?
3 hours
In a direct proportion, the ratio between two quantities is constant and can be expressed as kx
What is the constant of proportionality if each pencil costs £0.50?
0.50
In an inverse proportion, as one quantity increases, the other decreases
What happens to the product of two quantities in an inverse proportion?
It remains constant
In a direct proportion, two quantities increase or decrease at the same rate.
The equation for an inverse proportion is k/x
If 1 painter takes 6 hours to paint a wall, how long will 2 painters take?
3 hours
The constant of proportionality in an inverse proportion remains the same regardless of the quantities involved.
What is the constant of proportionality in the inverse proportion example with painters and time?
6
Two quantities are in direct proportion if they increase or decrease at the same rate
What does 'k' represent in the direct proportion equation y = kx?
Constant of proportionality
In an inverse proportion, the product of two quantities is constant.
Match the number of painters with the time taken to paint a wall in an inverse proportion example:
1 ↔️ 6 hours
2 ↔️ 3 hours
3 ↔️ 2 hours
In a direct proportion, the relationship between two quantities is represented as y = kx
As the number of painters increases, the time taken to paint a wall decreases in an inverse proportion.
How long will it take 2 painters to paint a wall if 1 painter takes 6 hours?
3 hours
To apply proportion in real-world scenarios, we use the concepts of direct proportion and inverse
In a direct proportion, the constant of proportionality is denoted by the letter k
If the cost of pencils is directly proportional to the number purchased, and each pencil costs £0.50, what is the constant of proportionality?
0.50
Arrange the table values for the cost of pencils if each pencil costs £0.50:
1️⃣ 1 pencil - £0.50
2️⃣ 2 pencils - £1.00
3️⃣ 3 pencils - £1.50
In an inverse proportion, as one quantity increases, the other quantity decreases
In an inverse proportion, the product of the two quantities remains constant.
Match the number of painters with the time taken to paint a wall in hours, assuming inverse proportion:
1 painter ↔️ 6 hours
2 painters ↔️ 3 hours
3 painters ↔️ 2 hours
In the inverse proportion example of painting a wall, what is the constant of proportionality?
6
In direct proportion, the formula is y = kx, where k is the constant of proportionality.
In inverse proportion, the formula is y = k/x, where k is the constant of proportionality
5 kg of sugar costs £12.50. How much will 8 kg of sugar cost, assuming direct proportion?
£20
If it takes 3 painters 8 hours to paint a house, it will take 4 painters 6 hours to paint the same house.