Direct Variation

• Direct variation


  A situation that produces pairs of numbers where the ratio is constant
• Equation of direct variation

  y = kx, where k is the constant of variation or constant of proportionality
• In direct variation, an increase in x causes an increase in y, and a decrease in x causes a decrease in y
• Illustrating direct variation

  1. Translate the situation into a variation statement

  2. Express the relationship as a mathematical equation

  3. Represent the relationship using a table of values

  4. Graph the relationship
• Examples of direct variation

  • Distance travelled vs time
  • Failure of a passenger vs distance of destination
  • Weight of an object vs its mass
  • Area of a triangle vs its height
• Finding the constant of variation and equation of variation

  1. Substitute known values into the equation y = kx

  2. Solve for the constant k

  3. Write the equation of variation as y = kx
• If y varies directly as x, and y = 24 when x = 6, then the constant of variation is 4 and the equation of variation is y = 4x
• If x varies directly as y, and x = 35 when y = 7, then the constant of variation is 5 and the equation of variation is x = 5y
• Solving problems involving direct variation

  1. Translate the problem into the equation of direct variation

  2. Substitute known values

  3. Solve for the unknown value
• Examples of direct variation problems

  • Worker's paycheck vs number of hours worked
  • Weight of an object on the moon vs weight on Earth
• If h is doubled in the equation t = 4h, then t is also doubled