Question

Graph the solution set. $$ y>-5 x+3 $$

   Graph the solution set.
$$
y>-5 x+3
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 3, Problem 16

Instant Answer

Solved by Expert Jennifer Stoner

03/10/2023

Step 1

The inequality $y > -5x + 3$ means that the y-values are greater than the line $y = -5x + 3$. Show more…

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Graph the solution set. $$ y>-5 x+3 $$

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Key Concepts

Linear Equations

A linear equation represents a straight line on a coordinate plane, typically expressed in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. This form helps in easily identifying the direction and position of the line on the graph.

Slope-Intercept Form

The slope-intercept form of a linear equation provides a clear understanding of how the line behaves. The slope (m) determines the steepness and direction, while the y-intercept (b) indicates where the line crosses the y-axis. In graphing, these components are essential for plotting the line accurately.

Graphing Inequalities

Graphing inequalities involves drawing a boundary line that represents the corresponding equality and then shading the region that satisfies the inequality condition. For strict inequalities, such as those with the '>' or '<' symbols, the boundary line is typically drawn as a dashed line to indicate that points on the line are not included in the solution set.

Half-Planes

The concept of half-planes comes into play when a line divides the coordinate plane into two regions. Each region, or half-plane, consists of all points on one side of the boundary line. Selecting the correct half-plane depends on testing a simple point (often the origin) to see if it satisfies the inequality.

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