DIRECT PROPORTION DIRECT VARIATION

Direct Proportion (Direct Variation)

Definition of Direct Proportion (Direct Variation)

Two quantities are said to be in direct proportion (or directly proportional), if one is a constant multiple of the other, i.e. y is said to be directly proportional to x if y = kx where k is a constant.

More about Direct Proportion (Direct Variation)

'y is directly proportional to x' is also written as y α x.

Example of Direct Proportion (Direct Variation)

Justin pays $40 per day for his stay in a hotel.
So, his rental charges depend upon the number of days he would stay in the hotel.
We write this direct variation as y = 40x, where y is the rental charges and x is the number of days that he would stay in the hotel.

Solved Example on Direct Proportion (Direct Variation)

A biscuit manufacturing company packs 26 packets per carton. Find the number of packets that can be packed in 2 cartons.
Choices:
A. 52
B. 26
C. 78
D. 104
Correct Answer: A

Solution:

Step 1: Let y be the number of biscuit packets and x be the number of cartons.
Step 2: Since the number of biscuit packets and the number of cartons vary directly, the equation is of the form y = kx .
Step 3: As each carton contains 26 biscuit packets, the constant of variation is 26.
Step 4: y = 26x [Substitute k = 26.]
Step 5: y = 26 × 2 [Substitute x = 2.]
Step 6: y = 52 [Multiply.]
Step 7: So, 52 biscuit packets can be packed in 2 cartons.

Related Terms for Direct Proportion (Direct Variation)

Multiple
Proportion
Variable

Quick Summary

Direct proportion means as one quantity increases, the other increases proportionally.
The relationship can be expressed as y = kx.
k is the constant of proportionality.

\[ y = kx \]

🍎 Teacher Insights

Use real-world examples to illustrate direct proportion, such as the relationship between hours worked and earnings, or the amount of ingredients needed for a recipe.

🎓 Prerequisites

Basic Algebra
Understanding of Variables
Concept of Constants

Check Your Knowledge

Q1: If y is directly proportional to x, and y = 10 when x = 2, what is the value of y when x = 5?

15 20 25 30

Q2: Which equation represents a direct proportion?

y = x + 2 y = 3x y = 5/x y = x^2

Frequently Asked Questions

Q: What does it mean when two quantities are directly proportional?
A: It means that as one quantity increases, the other quantity increases at a constant rate.

Q: How do you find the constant of proportionality?
A: Divide the value of y by the value of x (k = y/x).