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🔟elementary algebra review

key term - Direct Proportion

Citation:

Definition

Direct proportion is a relationship between two variables where one variable increases or decreases in direct relation to the other variable. In other words, as one variable changes, the other variable changes proportionally.

5 Must Know Facts For Your Next Test

  1. In a direct proportion, the ratio between the two variables is constant, meaning their relationship can be expressed as a linear equation.
  2. Direct proportion is often represented by the equation $y = kx$, where $k$ is the constant of proportionality.
  3. Direct proportion is a fundamental concept in solving problems involving similar figures, as the corresponding sides of similar figures are in direct proportion.
  4. The constant of proportionality, $k$, represents the rate of change between the two variables and can be calculated by dividing one variable by the other.
  5. Direct proportion is a key concept in understanding and solving applications of proportion, such as scale drawings, unit conversions, and rate problems.

Review Questions

  • Explain how direct proportion is used in the context of solving proportion and similar figure applications.
    • Direct proportion is a crucial concept in solving proportion and similar figure applications. When two quantities are in direct proportion, their relationship can be expressed as a linear equation, where one variable is proportional to the other. This allows for the use of proportions to solve for unknown values, such as finding the missing side lengths of similar figures. The constant of proportionality, $k$, represents the rate of change between the two variables and is a key component in setting up and solving these types of problems.
  • Describe how the concept of direct proportion can be used to solve scale drawing problems.
    • In scale drawing problems, the dimensions of the actual object and the dimensions of the scaled drawing are in direct proportion. The scale factor, which represents the ratio between the actual size and the scaled size, is the constant of proportionality. By setting up a proportion using the scale factor and the known dimensions, you can solve for the missing dimensions of the scaled drawing. This direct proportion relationship allows you to accurately determine the sizes of the scaled object based on the given information.
  • Analyze how the understanding of direct proportion can be applied to solve rate problems, such as those involving unit conversions or speed calculations.
    • Rate problems often involve direct proportion relationships. For example, in a unit conversion problem, the quantity in one unit is directly proportional to the quantity in another unit, with the conversion factor being the constant of proportionality. Similarly, in a speed problem, the distance traveled is directly proportional to the time elapsed, with the speed being the constant of proportionality. By recognizing these direct proportion relationships, you can set up and solve rate problems by using proportions to find the unknown values, such as the converted units or the time or distance traveled.