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What is the Direct Variation Equation that Relates the Two Variables?

Published in Mathematics 2 mins read

A direct variation equation describes a relationship where two variables increase or decrease proportionally. This means if one variable doubles, the other variable also doubles.

The general form of a direct variation equation is:

y = kx

Where:

  • y and x are the variables
  • k is the constant of variation

Understanding the Equation:

  • k represents the factor by which y changes for every unit change in x.
  • If k is positive, y increases as x increases.
  • If k is negative, y decreases as x increases.

How to Find the Equation:

  1. Identify the variables: Determine which two variables are related by direct variation.
  2. Find the constant of variation (k): Use a given pair of values for the variables (x, y) to solve for k in the equation y = kx.
  3. Write the equation: Substitute the value of k back into the general equation y = kx.

Example:

Suppose the distance traveled (d) varies directly with the time (t) spent traveling. If you travel 60 miles in 2 hours, what is the direct variation equation relating distance and time?

  1. Variables: Distance (d) and time (t)
  2. Constant of variation (k): We know d = 60 miles when t = 2 hours. Substitute these values into the equation d = kt:
    • 60 = k * 2
    • k = 60 / 2 = 30
  3. Equation: Substitute k = 30 back into the equation d = kt:
    • d = 30t

This equation tells us that for every hour traveled, the distance traveled increases by 30 miles.

Practical Insights:

  • Direct variation is common in real-world scenarios: Think about the relationship between the number of hours worked and the amount of money earned, or the number of items purchased and the total cost.
  • Understanding direct variation can help you make predictions: Once you know the equation, you can predict the value of one variable if you know the value of the other.

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