Understanding Direct Proportionality

Definition

• Two variables are directly proportional if as one variable increases, the other increases at the same rate.
• Example: Hours worked and amount earned can be directly proportional if the pay rate per hour is constant.

Example Explanation

• Scenario: Paid £12 per hour.
  • 1 hour = £12
  • 2 hours = £24 (twice the hours, twice the pay)
  • 10 hours = £120 (ten times the hours, ten times the pay)

Graphical Representation

• Characteristics of the Graph:
  • Always a straight line.
  • Passes through the origin (0,0).
• Axes Labels:
  • X-axis: Hours Worked
  • Y-axis: Money Earned

Using the Graph

• You can determine earnings for any time worked by plotting or drawing a line to the y-axis.
  • Example: 3.5 hours corresponds to £42.

Summary Points

• Directly proportional variables: Both increase or decrease proportionally.
  • If one variable doubles, the other doubles.
  • If one halves, the other halves.
• Graph of directly proportional variables is a straight line through the origin.

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