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Graphing Linear Inequalities in Two Variables: A Step-by-Step Guide, Exercises of Linear Algebra

Bridgewater State University (BSU)Linear Algebra

Learn how to graph linear inequalities in two variables by following these helpful steps. Understand the concept of boundary lines, shading regions, and how to graph inequalities not in slope-intercept form. Use this guide as study notes, summaries, or schemes and mind maps to prepare for exams.

Typology: Exercises

2021/2022

Uploaded on 09/12/2022

ekayavan
ekayavan 🇺🇸

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How to Graph a Linear Inequality In Two Variables
Vocabulary:
1. linear inequality (in two variables): relates two variables using an inequality symbol;
• its graph is a region of the coordinate plane bounded by a line
2. boundary line - line which divides the coordinate plane
into two regions;
• It defines the end of a solution of an inequality
Helpful Hints:
• Think of the underlines in the symbols ≤ and ≥ as representing solid lines on the graph.
• Use this chart to help you:
pf2

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Download Graphing Linear Inequalities in Two Variables: A Step-by-Step Guide and more Exercises Linear Algebra in PDF only on Docsity!

How to Graph a Linear Inequality In Two Variables

Vocabulary:

  1. linear inequality (in two variables): relates two variables using an inequality symbol;
    • its graph is a region of the coordinate plane bounded by a line
  2. boundary line - line which divides the coordinate plane into two regions;
  • It defines the end of a solution of an inequality

Helpful Hints:

  • Think of the underlines in the symbols ≤ and ≥ as representing solid lines on the graph.
  • Use this chart to help you:

• Inequality is in slope-intercept form: y ≤ m x + b

Steps Example

Step 1: Graph the boundary line:

  • Use Slope and Y-intercept: o Plot the y-intercept (b); (0, b)

o Slope (m) to find a 2nd^ point:

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟

  • Make a table with 3 points  Use a solid line for ≤ or ≥  Use a dashed line for < or >

Step 2: Shade the graph

  • Shade above the boundary line if the symbol is > 𝑜𝑜𝑜𝑜 ≥ (greater than or greater than or equal to)
  • Shade below the boundary line if the symbol is < 𝑜𝑜𝑜𝑜 ≤ (less than or less than or equal to)

y ≥ 2 x – 4

b= -

m = 2

  1. Boundary line is solid because it is greater than or equal to
  2. Shade above the graph because y is greater than or equal to.

• Equation is not in slope-intercept form:

Rearrange into slope-intercept form and follow above or

Steps Example

Step 1: Graph the boundary line:

  • Make a table with 3 points
  • Find the x & y- intercept

 Use a solid line for ≤ or ≥  Use a dashed line for < or >

Step 2: Pick a test point and shade (The point (0, 0) is the easiest point to test if it is not on the boundary line.)

  • If you get a TRUE statement with the test point, shade the same side of the boundary line that includes the test point
  • If you get a FALSE statement, shade the opposite side of the line
  1. Boundary line is dashed because it is less than
  2. Test Point (0, 0): −2(0) − 3(0) < 6 0 < 6 − 𝑖𝑖𝑖𝑖 𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡 Shade above the graph because test point was a true statement.

x y