Proportional relationships

• Proportional relationships describe a proportional connection between two variables
• This can happen in two ways
  • 

• Both direct and inverse proportion can be represented graphically
  • Direct proportion creates a linear graph where k is the gradient
  • Inverse proportion creates a reciprocal graph

Direct proportion

Inverse proportion?

• Be clear about what?y?is proportional to …
  • “… the square of?x” (x²)
  • “…?x?plus four” (x + 4)
• Calculate?or?deduce?the value of?k?from the information given or a graph
• Once you've found k sub it back in to your original proportion equation
• You can now find any values using this proportional relationship

• y = mx + c?rearranges to?y – c = mx?so (y - c) is?directly?proportional to?x
• Proportional?relationships?are often used in modelling