Linear inequalities in two variables show regions in a coordinate...
Mathematics48 views·Updated Jun 11, 2026·2 pagesUnderstanding Linear Inequalities in Two Variables
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River Przygoda@riverprzygoda_jvnr
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Graphing Linear Inequalities in Two Variables
When graphing a linear inequality like 6x - 3y > 18, first rearrange it into slope-intercept form. For this example, we get y < 2x - 6 by isolating y. The boundary line is y = 2x - 6, which we draw as a dashed line since the inequality uses < (not ≤).
To determine which side of the line to shade, we need to remember some key rules. For inequalities with y > or y ≥, shade above the line. For y < or y ≤, shade below the line. When given in the form ax + by > c or ax + by < c, test a point (like the origin) to determine which region to shade.
Different types of inequalities include horizontal lines (y < 4), vertical lines , and sloped lines . Each creates different shading regions based on the inequality symbol used.
Remember this! The boundary line is solid for ≤ or ≥ inequalities (inclusive) and dashed for < or > inequalities (exclusive). This shows whether points on the line itself are part of the solution.
2
of 2
Applications of Linear Inequalities
Linear inequalities help solve real-world problems with constraints. For example, if a vendor sells hot dogs for $4 and hamburgers for $5, and needs to make at least $1,000 in sales, we can write this as 4x + 5y ≥ 1000, where x represents hot dogs and y represents hamburgers.
By rearranging to y ≥ -4/5x + 200, we can graph this inequality. The boundary line is y = -4/5x + 200, and we shade above since the inequality is ≥. The shaded region shows all possible combinations of hot dogs and hamburgers that would generate at least $1,000 in sales.
The graph helps visualize that if the vendor sells no hamburgers , they would need to sell at least 250 hot dogs to reach the goal. Similarly, if they sell no hot dogs , they'd need to sell at least 200 hamburgers.
Pro tip: When solving real-world problems, pay attention to context constraints. For example, in this problem, you can't sell negative amounts of food, so the solution is limited to the first quadrant (where x ≥ 0 and y ≥ 0).
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Mathematics48 views·Updated Jun 11, 2026·2 pagesUnderstanding Linear Inequalities in Two Variables
R
River Przygoda@riverprzygoda_jvnr
Linear inequalities in two variables show regions in a coordinate plane where pairs of values satisfy a given condition. Just like linear equations form lines, linear inequalities create regions above, below, to the right, or to the left of lines....
1
of 2
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Graphing Linear Inequalities in Two Variables
When graphing a linear inequality like 6x - 3y > 18, first rearrange it into slope-intercept form. For this example, we get y < 2x - 6 by isolating y. The boundary line is y = 2x - 6, which we draw as a dashed line since the inequality uses < (not ≤).
To determine which side of the line to shade, we need to remember some key rules. For inequalities with y > or y ≥, shade above the line. For y < or y ≤, shade below the line. When given in the form ax + by > c or ax + by < c, test a point (like the origin) to determine which region to shade.
Different types of inequalities include horizontal lines (y < 4), vertical lines , and sloped lines . Each creates different shading regions based on the inequality symbol used.
Remember this! The boundary line is solid for ≤ or ≥ inequalities (inclusive) and dashed for < or > inequalities (exclusive). This shows whether points on the line itself are part of the solution.
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Applications of Linear Inequalities
Linear inequalities help solve real-world problems with constraints. For example, if a vendor sells hot dogs for $4 and hamburgers for $5, and needs to make at least $1,000 in sales, we can write this as 4x + 5y ≥ 1000, where x represents hot dogs and y represents hamburgers.
By rearranging to y ≥ -4/5x + 200, we can graph this inequality. The boundary line is y = -4/5x + 200, and we shade above since the inequality is ≥. The shaded region shows all possible combinations of hot dogs and hamburgers that would generate at least $1,000 in sales.
The graph helps visualize that if the vendor sells no hamburgers , they would need to sell at least 250 hot dogs to reach the goal. Similarly, if they sell no hot dogs , they'd need to sell at least 200 hamburgers.
Pro tip: When solving real-world problems, pay attention to context constraints. For example, in this problem, you can't sell negative amounts of food, so the solution is limited to the first quadrant (where x ≥ 0 and y ≥ 0).
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What is the Knowunity AI companion?
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Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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GeometryMath Flashcards: Triangles, Angles, and Congruent Triangles
Master the fundamentals of geometry with these math flashcards covering triangle angles, parallel lines, and congruent triangles. Test your knowledge and ace your exams!
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GeometryGeometry Flashcards: Triangles, Proofs, Angles, and Lines
Master the fundamentals of geometry with these flashcards covering triangles, proofs, angles, and parallel lines. Test your knowledge and ace your exams!
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GeometryGeometry Essentials
Master the fundamentals of geometry with these flashcards covering angles, triangles, congruent triangles, parallel lines, and polygons.
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Solve for x when there is x on both sides of equation.
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Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
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4.6/5App Store
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Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user