Question

Graph each inequality. $$ 5 x+3 y<10 $$

   Graph each inequality.
$$
5 x+3 y<10
$$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 4, Problem 18

Instant Answer

Solved by Expert Jerelyn Nevil

03/13/2023

Step 1

To do this, we subtract $5x$ from both sides of the inequality to isolate $3y$ on one side: $$3y < -5x + 10.$$ Show more…

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Graph each inequality. $$ 5 x+3 y<10 $$

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Key Concepts

Slope-Intercept Form

Converting the equation of the boundary line into slope-intercept form (y = mx + b) simplifies the process of graphing by clearly showing the slope and y-intercept. This form is particularly useful for quickly sketching the line and understanding its direction and positioning on the graph.

Shading Regions

Once the boundary line is drawn, a test point (commonly the origin if it is not on the line) is used to determine which side of the line satisfies the inequality. The region that meets the inequality condition is then shaded, visually representing all possible solutions.

Linear Inequalities

Linear inequalities involve expressions where a linear combination of variables is compared to a constant using inequality symbols (such as <, >, ?, or ?). In the context of graphing, the inequality divides the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Boundary Lines

The boundary line is created by replacing the inequality sign with an equality. This line represents the limit at which the inequality changes its status. For strict inequalities (like < or >), the boundary line is usually drawn as a dashed line to indicate that points on the line are not included in the solution set.

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