Proportional relationships

• Proportional relationships describe a proportional connection between two variables
• This can happen in two ways
  • Direct proportion
    • one variable increases or decreases the other does the same
  • Inverse proportion
    • one variable increases the other decreases and vice versa
• Proportional relationships use the symbol ?which means is proportional to

• 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

• means y is proportional to x
• y?increases as?x?does,?k?determines the?rate?(gradient)
• by changing this to the equation ?we can substitute in given values and solve to find k
  • Note that this means the?ratio?of x and y is constant?k = y / x

  

Inverse proportion

• means y is proportional to ?or y is inversely proportional to x
• y?decreases as?x?increases and vice versa,?k?determines the rate
• by changing this to the equation ?we can substitute in given values and solve to find k
  • Note that this means the?product?of x and y is constant?k = xy?

How do I work with proportional relationships?

• Set up your proportional relationship using ?then change to = k
• Be clear about what?y?is proportional to …
  • “… the square of?x”
  • “…?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