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Writing the Inequality from Its Graph
When deducing the linear inequality from a graph with the boundary line , one must inspect the line style and the location of the shaded region. The graph displays a solid boundary line, meaning the inequality must include an equal sign, taking the form of or . To decide which symbol is correct, test a point such as the origin . If the origin is located in the unshaded section of the coordinate plane, substituting and into the expression must result in a false statement. The evaluation gives . Because the unshaded region must yield a false statement for the correct inequality, and is false, the inequality describing the shaded solution region is .
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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A facility manager uses the inequality 2x + 3y < 6 to represent the maximum weight capacity for two types of equipment in a storage unit. On the graph of this inequality, what does the dashed boundary line 2x + 3y = 6 indicate?
A logistics coordinator is identifying the inequality 2x + 3y < 6 from a graph. A dashed boundary line indicates that the points on the line 2x + 3y = 6 are excluded from the solution set.
A project manager uses a coordinate graph to monitor the use of two different resources, x and y. The allowed combinations are defined by the inequality 2x + 3y < 6. Match each graphical element with its corresponding mathematical meaning in this scenario.
A project manager is identifying the linear inequality $2x + 3y < 6$ from a graph provided in a resource report. Arrange the following steps in the correct order to determine this inequality using the test-point method.
A budget analyst is verifying a graph that represents the spending limit $2x + 3y < 6. To confirm which side of the boundary line $2x + 3y = 6 should be shaded, the analyst substitutes the coordinates into the inequality. This specific verification technique is known as the ________ method.
Identifying Inequalities from Visual Cues
Interpreting Dashboard Resource Constraints
Procedural Review of Capacity Graphs
An inventory coordinator is reviewing a resource constraint graph where the boundary line is defined by the equation $2x + 3y = 6(0,0)$. Which inequality is correctly represented by this graph?
A production planner is verifying a resource constraint graph represented by the inequality $2x + 3y < 6(0, 0) as a test point, the planner determines that the resulting statement ($0 < 6) is true. According to the standard rules of the test-point method, what does this 'true' result indicate about the graph's shading?
Writing the Inequality from Its Graph
Writing the Inequality from Its Graph
Learn After
A project manager uses a graph to monitor resource constraints where the boundary is represented by the solid line . If the origin is located in the unshaded region, which of the following correctly describes the rule for determining that is the correct inequality for the shaded region?
An operations analyst is evaluating a resource allocation graph bounded by the solid line . To identify the correct inequality, the analyst tests the origin point , which lies in the unshaded region. Because the origin is located in the unshaded region, substituting and into the correct inequality must produce a ____ statement.
A project manager is using a graphical model to track resource constraints where the boundary is defined by the solid line . Arrange the following steps in the correct logical order to determine that the shaded solution region is represented by the inequality .
In logistics and resource management, constraint boundaries are often graphed as linear inequalities. For a constraint graph bounded by the line , match each graphical component with its specific role in determining the correct inequality, such as .
In a production constraint model represented by a graph, the use of a solid boundary line for the equation indicates that the points located on the line are included in the solution set for the inequality .