Boundary Lines for Single-Variable Inequalities on the Coordinate Plane
Some linear inequalities involve only one variable — they contain but not , or but not . When such an inequality is graphed on the coordinate plane rather than on a number line, the boundary line takes a special form:
- produces a vertical boundary line passing through every point whose x-coordinate is .
- produces a horizontal boundary line passing through every point whose y-coordinate is .
Once the boundary line is drawn (solid or dashed, depending on whether the inequality includes the equal sign), the same test-point-and-shade procedure used for two-variable inequalities determines which side of the line to shade.
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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 to visualize team capacity. Arrange the following steps in the correct order to identify the equation of the boundary line for this constraint.
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A logistics manager uses the inequality to ensure a delivery van does not exceed its weight capacity, where represents standard boxes and represents heavy crates. When graphing this constraint, the manager identifies the boundary line . 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?
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Graphing the Linear Inequality
Learn After
Graphing
An inventory manager uses a coordinate grid to define storage sections in a warehouse. If a section boundary is represented by the equation x = 10, what is the orientation of this line on the grid?
A logistics coordinator is using a coordinate system to define shipping zones on a regional map. Match the following boundary line equations with their correct visual orientation on the map.
A landscape architect is using a coordinate grid to design a park layout. If the northern boundary of a play area is defined by the equation y = 30, the orientation of this boundary line on the grid is ____.
A safety officer is using a coordinate grid to define a 'no-go' zone in a factory. True or False: To establish a boundary using the inequality , the officer must draw a horizontal boundary line on the grid.
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A zoning technician is updating a municipal map to show areas with building height restrictions, often defined by inequalities like feet. To graph this boundary correctly on a coordinate plane, arrange the following steps in the standard order of operations.
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A facility technician is mapping a data center's floor plan on a coordinate grid. A main power conduit is installed along a boundary line represented by the equation . Which statement correctly describes the coordinates of every point located on this conduit?
A traffic engineer is using a coordinate grid to define a 'no-parking' zone at a busy intersection. The boundary line for this zone is represented by the equation . Which statement correctly describes the orientation and coordinate property of this boundary line?