Concept of Direct Proportion Direct proportion is a mathematical relationship between two numerical quantities where the ratio of the two quantities is cons...
Concept of Direct Proportion
Direct proportion is a mathematical relationship between two numerical quantities where the ratio of the two quantities is constant. This means that the product of the two quantities is equal to a constant value. The constant value represents the proportional relationship between the two quantities.
Example:
If the ratio of 3 and 15 is equal to 5, it means that for every 15 units, 3 units are required. Therefore, the direct proportion between 3 and 15 is 5.
Formal Definition:
Let a and b be two real numbers, where a and b are not equal to 0. Then, the direct proportion between a and b is established if:
a/b = k
where k is a constant.
Graphical Representation:
The direct proportion between a and b is represented by a line that passes through the origin. The slope of this line is equal to k.
Examples:
If the ratio of 4 and 8 is 2, then the direct proportion between 4 and 8 is 2.
If the ratio of 12 and 30 is 0.4, then the direct proportion between 12 and 30 is 0.4.
If the ratio of 10 and 20 is 2, then the direct proportion between 10 and 20 is 2