CIE A Level Maths: Pure 1复习笔记1.4.4 Proportional Relationships

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