Question

Graph the solution set. $$ -4 x \leq 12-3 y $$

   Graph the solution set.
$$
-4 x \leq 12-3 y
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 3, Problem 41

Instant Answer

Solved by Expert Jennifer Stoner

03/11/2023

Step 1

We start with the given inequality: $$ -4x \leq 12 - 3y $$ Show more…

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Graph the solution set. $$ -4 x \leq 12-3 y $$

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Key Concepts

Slope-Intercept Form

Rewriting the linear equation in slope-intercept form, y = mx + b, makes it easier to graph the line by clearly identifying the slope and y-intercept. This step is crucial when graphing the boundary line of the inequality as it provides a straightforward method for sketching the line accurately.

Linear Inequalities in Two Variables

This concept involves working with inequalities that relate two variables, typically x and y. It requires understanding how the inequality symbol affects the relationship between the variables, determining the boundary where the inequality holds as an equality, and then identifying which portion of the coordinate plane represents the solution set.

Graphing Inequalities on the Coordinate Plane

Graphing an inequality requires plotting a line corresponding to the boundary equation (obtained by setting the inequality to equality) on the coordinate plane, and then shading the region that satisfies the inequality. This process entails testing a point not on the line to determine which side of the boundary is included in the solution set.

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