Graphing Linear Inequalities

Overview

• Learn how to graph linear inequalities.
• Five problems increasing in difficulty.
• Discuss solution sets.
• Handle lines not in y=mx+b form.
• Interactive problem for viewers.
• Printable notes available in the video description.

Graphing Inequalities

Problem 1: y ≥ -2

• Graph the line: y = -2
  • y controls vertical position (y-axis).
  • A horizontal line representing y = -2.
• Inequality: y is greater than or equal to -2
  • Shade the region above the line.

Problem 2: x < 4

• Graph the line: x = 4
  • x controls horizontal position.
  • A vertical dotted line at x = 4 because x cannot equal 4.
• Inequality: x is less than 4
  • Shade the region to the left of the line.

Problem 3: y ≥ x + 3

• Form: y = mx + b, slope (m) = 1, y-intercept (b) = 3
• Graph the line: y = x + 3
  • Solid line because of '≥'.
  • Start at y-intercept (0,3), slope of 1 (up 1, right 1).
• Inequality: y is greater than or equal to x + 3
  • Shade the region above the line.

Problem 4: y < 2x - 4

• Slope and intercept: m = 2, b = -4
• Graph the line: y = 2x - 4
  • Dotted line (y cannot equal 2x - 4).
  • Start at y-intercept (0,-4), slope of 2 (up 2, right 1).
• Inequality: y is less than 2x - 4
  • Shade the region below the line.
• Solution set: All (x, y) pairs in the shaded region.
  • Example check: Point (5,4) is in the solution set.
  • Point (0,-1) is not.

Problem 5: 3y ≤ 6 - x

• Reform the inequality: y ≤ -1/3 x + 2
• Graph the line: y = -1/3x + 2
  • Solid line because of '≤'.
  • Start at y-intercept (0,2), slope of -1/3 (down 1, right 3).
• Inequality: y is less than or equal to -1/3x + 2
  • Shade the region below the line.

Interactive Problem

• Graph: x - 2y < 8
  • Determine if it should be a solid or dotted line.
  • Identify slope and y-intercept.
  • Decide shading direction.
• Comment a solution with one point in and one outside the solution set.

Additional Resources

• Printable notes with QR codes available in description.
• Subscribe for more content.

Conclusion

• Quick review of graphing linear inequalities.
• Encouragement to engage with provided practice problem.
• Notes and subscription reminder.