Question

Graph each inequality. $$ y<\frac{2}{5} x-3 $$

   Graph each inequality.
$$
y<\frac{2}{5} x-3
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 3, Problem 32

Instant Answer

Solved by Expert Erika Bustos

02/17/2022

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The slope is $\frac{2}{5}$ and the y-intercept is $-3$. Show more…

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Graph each inequality. $$ y<\frac{2}{5} x-3 $$

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Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation, written as y = mx + b, simplifies the process of graphing by clearly indicating the slope (m) and the y-intercept (b) of the line. This form aids in quickly identifying key points on the graph, which is especially useful when graphing inequalities.

Linear Inequalities

A linear inequality expresses a relation using <, >, ?, or ? in a linear equation, representing a set of solutions that form a half-plane on the coordinate grid rather than a single line. It is essential to understand that the inequality indicates which side of the boundary is included in the solution set.

Graphing Boundary and Shading

When graphing a linear inequality, the boundary line is first graphed using the slope-intercept form. For strict inequalities (using < or >), the boundary line is drawn as a dashed line to show that points on the line are not included in the solution. The corresponding half-plane on the side that satisfies the inequality is then shaded to complete the representation.

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