Algebra 1 Unit 7 Lesson 13 Graphing Linear Inequalities M-5
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This document provides instructions for graphing linear inequalities. It reviews graphing lines in slope-intercept form and includes the slopes of 2/3 and -1/4 as examples. It also explains that when the inequality symbol is > or ≥, the region above the line should be shaded, while < or ≤ means the region below the line should be shaded.
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Algebra 1 Unit 7 Lesson 13 Graphing Linear Inequalities M-4
This document provides instructions for graphing linear inequalities. It reviews graphing lines in slope-intercept form and defines the symbols for greater than, greater than or equal to, less than, and less than or equal to. It explains that when graphing inequalities, the region that satisfies the inequality is shaded, and whether to shade above or below the line depends on the inequality symbol used.
Graphing Linear Inequalities
- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
3 5 graphing linear inequalities in two variables
This document discusses how to graph linear inequalities in two variables. It explains that linear inequalities contain x and y variables separated by an inequality symbol (<, >, ≤, ≥) and the boundary is a straight line. To check if a point is a solution, plug it into the inequality and see if it makes a true statement. Examples are provided of checking points for different inequalities. The document also discusses using solid vs dashed boundary lines depending on the inequality symbol and shading the correct side of the boundary line based on a test point. Methods for graphing simple one-variable inequalities and inequalities written in slope-intercept and standard form are presented along with examples.
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This document discusses linear inequalities and how to graph them. It introduces linear inequalities as expressions with inequality symbols like <, >, ≥, or ≤ instead of equals signs. Solutions to inequalities are ordered pairs that make the statement true. It explains how to check if a point is a solution, and how to graph inequalities by treating them as equalities and shading the correct side based on the inequality symbol and a test point. The document contains examples of graphing various one-variable and two-variable inequalities.
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This document discusses how to graph linear inequalities on a coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. It notes that inequalities must be written in slope-intercept form before graphing and that the shading depends on whether the inequality involves less than or greater than. Specifically, y greater than inequalities are shaded above the line and y less than inequalities are shaded below the line. Practice graphing many problems to fully understand how to determine the shading direction.
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This document discusses an alternative way to solve compound linear inequalities that makes the process easier to learn. It presents the method through clear examples and step-by-step instructions. Solving inequalities using this approach helps students learn more quickly and easily understand the material by clearly explaining the examples, instructions, and steps in a way that students can easily remember and apply the problem-solving process.
Solving linear inequalities
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Alg1 7.13 Graphing Linear Inequalities
This document provides instructions for graphing linear inequalities on a coordinate plane. It reviews graphing linear equalities and defines the four types of inequalities: less than, greater than, less than or equal to, and greater than or equal to. Examples of individual inequalities are given, such as y > 5 and x ≤ 3. The document explains that the solution to an inequality includes all points on or within the boundary line. It poses questions about graphing an inequality line, including identifying the y-intercept, slope, border, shading, solutions and non-solutions.
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Algebra 1 Unit 7 Lesson 13 Graphing Linear Inequalities M-4
This document provides instructions for graphing linear inequalities. It reviews graphing lines in slope-intercept form and defines the symbols for greater than, greater than or equal to, less than, and less than or equal to. It explains that when graphing inequalities, the region that satisfies the inequality is shaded, and whether to shade above or below the line depends on the inequality symbol used.
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- A linear inequality describes a region of the coordinate plane bounded by a line. Any point in the shaded region is a solution to the inequality.
- To graph a linear inequality, first solve it for y and graph the resulting equation as a line. Then, test a point not on the line to determine which side of the line to shade based on whether it satisfies the inequality.
- The line is drawn solid for ≤ or ≥ and dashed for < or >. Shading the correct side of the line indicates the full solution set of the inequality.
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This document discusses how to graph linear inequalities on a coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. It notes that inequalities must be written in slope-intercept form before graphing and that the shading depends on whether the inequality involves less than or greater than. Specifically, y greater than inequalities are shaded above the line and y less than inequalities are shaded below the line. Practice graphing many problems to fully understand how to determine the shading direction.
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This document discusses an alternative way to solve compound linear inequalities that makes the process easier to learn. It presents the method through clear examples and step-by-step instructions. Solving inequalities using this approach helps students learn more quickly and easily understand the material by clearly explaining the examples, instructions, and steps in a way that students can easily remember and apply the problem-solving process.
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This document discusses solving systems of linear inequalities. It begins with examples of graphing two-inequality systems by shading the regions defined by each inequality boundary and finding the overlapping solution region. It also covers checking solutions by testing points. Applications include painting plates within cost and number limits and geometry shapes defined by inequalities. The document emphasizes representing "greater than" or "less than" situations with systems of inequalities and using graphing to find the solution region.
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The document discusses linear inequalities in two variables and their graphical representations. It introduces the Cartesian coordinate system developed by Rene Descartes and its importance. It explains how to graph linear inequalities by first drawing the line as an equation, then determining whether to shade above or below the line based on whether a test point satisfies the inequality. Students are assigned to bring graphing paper, coloring materials, and a ruler to class on Monday to graph linear inequalities.
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