Question

Write an inequality for each graph.

   Write an inequality for each graph.

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 2, Problem 38

Instant Answer

Solved by Expert Taylor Shimono

08/11/2019

Step 1

Since this is not a straight horizontal or vertical line, we will use the slope-intercept form. We can see that the y-intercept is at 2, so our b value in the slope-intercept form will be 2. Show more…

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Write an inequality for each graph.

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Key Concepts

Linear Inequalities

Linear inequalities involve expressions where two linear expressions are related by an inequality symbol (such as <, >, ?, or ?) rather than an equality sign. They define regions on a number line or coordinate plane that represent all the solutions that satisfy the inequality.

Graphical Representation of Inequalities

Graphing an inequality on the coordinate plane involves drawing a boundary line, which represents where the equality holds, and then shading the region that satisfies the inequality. The chosen shading indicates all points (x, y) that make the inequality true.

Boundary Lines

The boundary line in the graph of an inequality represents the set of points where the expression equals the constant term. A solid boundary line is used if the inequality includes equality (? or ?), while a dashed line is used if the inequality is strict (< or >), indicating that points on the line are not included in the solution.

Test Point Method

The test point method is a common technique for determining which side of the boundary line should be shaded when graphing an inequality. By selecting a point not located on the boundary line and substituting it into the inequality, one can verify whether the point satisfies the relationship, thereby identifying the correct region.

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