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Writing the Inequality from Its Graph
When identifying the linear inequality from a graph that features a solid boundary line defined by the equation and a shaded upper-right half-plane, one applies the test-point method. By selecting the origin , which is located in the unshaded lower-left portion of the coordinate plane, substituting and should logically result in a false mathematical statement for the final inequality. Evaluating the 'greater than or equal to' relationship yields , which simplifies to . Since this is a demonstrably false statement, the unshaded region containing represents the false side of the inequality. Consequently, the opposite, shaded half-plane represents the true solution set for the inequality . The use of a solid boundary line visually confirms that the boundary values themselves are included in the solution set.
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Writing the Inequality from Its Graph
Writing the Inequality from Its Graph