ACCA MA Syllabus B. Data Analysis And Statistical Techniques - Linear functions and equations - Notes ^{1 / 12}

Equation of a straight line: y = a + bx

The equation of a straight line is y = a + bx

‘a’ – the intercept, i.e. the value of y when x = 0
‘b’ – the gradient of the line y = a +bx (the change in y when x increases by one unit)
‘x’  - the independent variable
‘y’ – the dependent variable

‘a’  is the fixed cost per period
‘b’ is the variable cost per unit
‘x’ is the activity level
‘y’ is the total cost = fixed cost +  variable cost

Illustration

Y = 10,000 + 50X

What is the total cost of 500 units and 700 units?

• Solution:

  y = 10,000 + 50 x 500
  y = $35,000 is the total cost at 500 units.

  y = 10,000 + 50 x 700
  y = $45,000

  Therefore, we can see that the change in cost between these two levels of activity is $45,000 - $35,000 = $10,000