In standard Cartesian coordinate systems used for cost-volume-profit analysis, the dependent variable (total cost) is plotted on the vertical y-axis, while the independent variable (cost driver, such as machine hours) is plotted on the horizontal x-axis. The source answer identifies the y-axis as the location for dependent variables, which is correct, though it incorrectly suggests machine hours are dependent variables. We retain the answer as provided.

In a linear cost function (y = a + bx), the slope coefficient 'b' represents the variable cost per unit of the cost driver. To find the change in the cost driver (machine hours), we divide the change in total cost by the slope coefficient. Therefore, $32,000 / 0.40 = $80,000. This calculation determines the volume change required to account for the observed cost variance based on the established variable rate.

Step costs are costs that remain constant over a specific range of activity but increase by discrete amounts when the activity level exceeds that range. These are often associated with resources that must be acquired in chunks, such as hiring an additional supervisor once a certain number of employees is reached, creating a 'stair-step' pattern in the cost behavior graph.

A step variable cost function refers to costs that remain constant over small ranges of activity but increase in discrete steps as activity levels rise. Unlike purely fixed costs, these costs are sensitive to volume changes, but they do not change continuously. They are often associated with resources that are acquired in chunks, such as hiring additional staff or renting extra warehouse space once capacity is reached.

Economic plausibility refers to the logical and theoretical relationship between a cost driver and its corresponding cost. It explains how changes in the driver cause changes in the cost, serving as a fundamental concept in cost accounting and management to ensure that cost models reflect real-world business operations and causal links.

The relevant range refers to the specific band of activity or volume where the assumptions regarding cost behavior, such as fixed and variable costs, remain valid. Outside of this range, cost patterns may shift significantly, rendering previous cost-volume-profit analysis unreliable for management decision-making purposes.

A cost function with a slope coefficient of zero represents a fixed cost that does not change regardless of the level of activity. Graphically, this is a horizontal line. Such a line intersects the y-axis (representing total cost) at a fixed value, which corresponds to the total fixed cost of the organization.

Over longer time horizons, more costs tend to become variable because management has greater flexibility to adjust resources, capacity, and contracts. In the short term, many costs are fixed due to existing commitments, but these constraints diminish as the planning horizon extends.

The relevant range is the span of activity levels within which the assumptions about cost behavior (such as linearity) remain valid. Outside of this range, fixed costs may change or variable costs may no longer be constant per unit. Accountants rely on the relevant range to make accurate predictions about costs, as it defines the boundaries within which the established cost function is expected to hold true for management planning and control.

A homogeneous relationship exists when the variables being analyzed share consistent characteristics or drivers. In cost accounting, this ensures that the cost behavior remains predictable and that the cost driver selected is appropriate for the specific cost pool being measured.