Direct Proportion Direct proportion is a special type of proportional relationship where the ratio of two corresponding measures remains constant. This means...
Direct proportion is a special type of proportional relationship where the ratio of two corresponding measures remains constant. This means that, regardless of the size of the two measures, their ratio will always be equal. For example, let's say we have two sets of measurements:
Set 1: { (2, 4), (4, 8), (6, 12) }
Set 2: { (1, 3), (2, 6), (3, 9) }
These two sets exhibit a direct proportion, as their ratios are equal. In this case, the ratio of any two measures is the same, which is 2:4=4:8.
Here's the formal definition:
If two variables are directly proportional, their ratio is equal to a constant k. This means that:
k = ratio = ratio/constant
In our example, k = 2, meaning that the ratio of any two measures is always 2.
Key points about direct proportion:
The constant k is always positive.
A constant k represents a fixed relationship between the two measures.
Any point on the line of proportionality corresponds to a specific ratio.
If the ratio is known, we can find the other measure by multiplying the constant by the known measure.
Examples:
Buying 3 shirts for $10 is directly proportional.
Walking 4 kilometers takes 8 minutes at a constant pace.
The number of pages in a book and the number of chapters in that book are directly proportional.
By understanding direct proportion, we can predict the value of one measure based on the value of the other, regardless of the size of the measures