Proportional Relationships (Cambridge (CIE) AS Maths): Revision Note

Proportional Relationships

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 

    

     

• Set up your proportional relationship using then change to = k

• 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