Question

Graph the solution set of each inequality. $$y<2 x+7$$

   Graph the solution set of each inequality.
$$y<2 x+7$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 8, Problem 48

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Solved by Expert Vipender Yadav

04/20/2020

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We can choose any values for $x$, but for simplicity, let's choose $x=0$ and $x=1$. Show more…

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Graph the solution set of each inequality. $$y<2 x+7$$

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Key Concepts

Linear Inequality

A linear inequality is an inequality that involves a linear function. It shows a relationship between variables that is less than, greater than, less than or equal to, or greater than or equal to. Instead of expressing a single line, the inequality represents a region of the coordinate plane where all the points satisfy the condition of the inequality.

Graphing Regions

Graphing a linear inequality involves drawing the corresponding boundary line and then shading the region that represents the solution set. The shading indicates all the points that satisfy the inequality. This process typically includes determining which side of the boundary line to shade by testing a point not on the line.

Slope-Intercept Form

The slope-intercept form of a linear equation, written as y = mx + b, where m is the slope and b is the y-intercept, is a useful format for graphing lines. It provides a straightforward way to identify how steep the line is and where it crosses the y-axis, making it easier to draw the corresponding line on a coordinate plane.

Boundary Line Representation

When graphing inequalities, the boundary line represents the equality part of the inequality. For strict inequalities (using < or >), the boundary line is drawn as a dashed line to indicate that points on the line are not included in the solution set, while for inclusive inequalities (using ? or ?), the line is drawn solid to show that the points on the line are part of the solution.

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