Direct and Indirect Proportion
This page covers the concepts of direct and indirect proportion, their equations, and practical applications in mathematics. It provides clear definitions, examples, and problem-solving techniques for both types of proportional relationships.
Direct proportion is explained as a relationship where two or more things are linked so that as one changes, the other changes in the same way. The equation y = kx represents this relationship, where k is the constant of proportionality.
Definition: Direct proportion is when two values are linked so that as one changes, the other changes in the same way, represented by the equation y = kx.
Indirect proportion is described as a relationship where two or more things are linked so that as one changes, the other changes in the opposite way. The equation y = k/x represents this relationship.
Definition: Indirect proportion is when two values are linked so that as one changes, the other changes in the opposite way, represented by the equation y = k/x.
The page emphasizes the importance of the constant of proportionality calculation in both types of proportion. For direct proportion, dividing the values yields this constant.
Highlight: The constant of proportionality (k) is crucial in both direct and indirect proportion equations and can be calculated by dividing the corresponding values.
Two detailed examples are provided to illustrate problem-solving techniques for direct and indirect proportion:
- Direct proportion example: Finding y when x changes, given initial values and the proportional relationship.
Example: y is directly proportional to x. When x = 3, y = 7.5. Find y when x = 4.4.
Solution steps:
- Write the equation: y = kx
- Find k: 7.5 = k(3), so k = 2.5
- Use the new x value: y = 2.5(4.4) = 11
- Indirect proportion example: Finding y when x changes, given initial values and the inverse proportional relationship.
Example: y is indirectly proportional to x. When x = 6, y = 8. Find y when x = 9.
Solution steps:
- Write the equation: y = k/x
- Find k: 8 = k/6, so k = 48
- Use the new x value: y = 48/9 = 16/3
The page concludes by mentioning that proportionality can also involve variations of x, such as x², and that the problem-solving approach remains similar for these cases.
Highlight: Proportional relationships can involve variations of x (e.g., x², √x), but the problem-solving approach remains consistent.
