Question

Graph each inequality. $$3 x-6 y \leq 12$$

   Graph each inequality.
$$3 x-6 y \leq 12$$

Algebra and Trigonometry

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 8, Problem 2

Instant Answer

Solved by Expert Ankit Gupta

06/10/2020

Step 1

To do this, we set y equal to zero and solve for x. $$3x - 6(0) \leq 12$$ $$3x \leq 12$$ $$x \leq 4$$ So, the x-intercept is (4,0). Show more…

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Graph each inequality. $$3 x-6 y \leq 12$$

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Key Concepts

Boundary Line

The boundary line of a linear inequality is the line obtained by replacing the inequality sign with an equality sign. For inclusive inequalities (? or ?), the boundary line is drawn as a solid line to indicate that points on the line are included in the solution set, while for strict inequalities (< or >), a dashed line is used instead.

Graphing Procedure

Graphing a linear inequality involves first drawing the boundary line on the coordinate plane, then selecting a test point from one side of the line to determine which region satisfies the inequality. The solution region is then shaded to visually represent all the points that meet the inequality condition.

Linear Inequalities

A linear inequality involves expressions that form a straight line when graphed, but instead of an equals sign, an inequality sign is used. This type of expression designates one side of the boundary line as the solution set, depending on whether the inequality is strict (< or >) or inclusive (? or ?).

Slope-Intercept Form

Converting a linear expression to slope-intercept form (y = mx + b) makes graphing easier by clearly showing the slope (m) and y-intercept (b). This format helps in quickly identifying the direction and position of the line on a coordinate plane.

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