Dashed and Solid Boundary Lines

Boundary Lines for Single-Variable Inequalities on the Coordinate Plane

A retail manager uses the inequality 20x + 15y <= 1200 to stay within the weekly budget for staffing, where x represents senior staff hours and y represents junior staff hours. To graph this budget constraint, the manager must first identify the boundary line. Which equation represents the boundary line for this inequality?

A production supervisor uses the inequality 15x + 20y <= 600 to model labor hours for two different assembly lines. To begin graphing this constraint, the supervisor identifies the line 15x + 20y = 600. This line, which separates the combinations that fit the budget from those that do not, is known as the ____ line.

A production supervisor uses the inequality 5x + 12y <= 600 to manage the hours required for two different assembly lines. To begin graphing this constraint, the supervisor identifies the boundary line. True or False: The boundary line for this inequality is represented by the equation 5x + 12y = 600.

An operations manager is analyzing several business constraints represented by linear inequalities. Match each constraint to the specific equation that represents its boundary line.

A project lead is graphing a resource constraint represented by the inequality $20x + 25y \leq 1000$ to visualize team capacity. Arrange the following steps in the correct order to identify the equation of the boundary line for this constraint.

Determining the Boundary Line for Budget Constraints

Defining the Boundary Line in Capacity Planning

Visualizing Production Capacity

A logistics manager uses the inequality $5x + 10y \leq 500$ to ensure a delivery van does not exceed its weight capacity, where $x$ represents standard boxes and $y$ represents heavy crates. When graphing this constraint, the manager identifies the boundary line $5x + 10y = 500$. According to the definition of a boundary line, what is its primary geometric function on the coordinate plane?

A logistics manager is mapping out delivery zones using a linear inequality in two variables. When the manager graphs the boundary line for a specific zone, the entire coordinate plane is divided into two distinct regions. According to the definition of a boundary line, what are these two regions called?

Procedure for Determining a Linear Inequality in Two Variables from its Graph

Graphing the Linear Inequality $y > x + 4$