Answer:
Proportionality describes a relationship between values that have the same ratio.
Direct Proportionality
The are 2 types of proportionality; the first is directly proportional. If a relationship is directly proportional, both values will increase or decrease together at the same rate. Directly proportional relationships are described by the equation:
In this equation, y and x are variables while k represents the constant of proportionality. In a directly proportional relationship, both the y and x value grow at the same rate. For example, take this set of values:
- y = {20, 40, 80}
- x = {2, 4, 8}
These values are directly proportional because they both double each time, meaning they grow at the same rate. Additionally, the ratio between terms remains the same. Take the ratios 20:2 and 40:4, when simplified these are both 10:1 (for proportionality it's easier to write ratios as y:x). Since the ratio is the same, they are proportional. Additionally, the ratio tells us that the constant of proportionality is 10. So the equation to represent this situation is
Indirectly Proportional
Indirect proportionality is similar to direct, but instead of increasing or decreasing together, one value increases while the other decreases. Indirect proportionality is described by the equation:
We can represent this with another set of x and y values.
- x = {1, 2, 5}
- y = {10, 5, 2}
Unlike directly proportional relationships, the growth rate is not constant. Still, we can represent this relationship as
.
So, k still equals 10, but the relationship is indirectly proportional. As x increases, y decreases, and vice versa.