Final answer:
The variable cost per unit of output is represented by the slope parameter in a linear equation, which in the discussed scenario, is the hourly rate charged by an auto mechanic in addition to a flat fee.
Step-by-step explanation:
The variable cost per unit of output corresponds to the slope parameter in the linear equation ลท = a + bx, where y represents the total variable cost, a is the fixed cost (intercept), and b is the variable cost per unit of output (slope). This is evident in the given scenario where an auto mechanic charges a flat fee (fixed cost) plus an hourly rate (variable cost). Here, the hourly rate represents the variable cost per unit of labor (the independent variable), which changes in proportion to the hours worked.
For example, in the provided information, the labor charge equation is y = 55x + 75, where 55 represents the variable cost per hour (slope) and 75 is the flat fee (intercept). This linear equation helps in calculating the total charge for labor based on the hours worked (independent variable), showing the direct relationship between labor time and total cost.