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How Do You Figure Out Whether a Boundary is a Part of the Graph of an Inequality?

Determine if the boundary is part of the graph of the inequality y≥2x-2

Summary

  1. The boundary is the line in the graph of an inequality
  2. '≥' means GREATER THAN OR EQUAL TO
  3. Since we have a GREATER THAN OR EQUAL TO sign, we have a SOLID line
  4. Plug the point (0,-2) into y≥2x-2 to see if it makes a true statement
  5. -2≥-2 is a true statement, so the boundary IS included in the graph of y≥2x-2
  6. Plug the same point (0,-2) into y>2x-2 to see if it makes a true statement
  7. -2>-2 is NOT a true statement, so the boundary is NOT included in the graph of y>2x-2

Notes

    1. Our inequality is y≥2x-2
    2. The '≥' symbol means GREATER THAN OR EQUAL TO'
    1. The line we draw for the graph of our inequality is called the BOUNDARY
    2. It will be solid or dashed depending on what our inequality symbol is
    3. The symbol in our inequality is ≥, or GREATER THAN OR EQUAL TO
    1. The '≥' symbol means GREATER THAN OR EQUAL TO'
    2. Since we have a GREATER THAN OR EQUAL TO symbol, we have a SOLID line
    3. But if we had just a GREATER THAN symbol, without the equal to, we would have a DASHED line
    1. We need to plug a point on the line into our inequality to see if the boundary is included in our graph
    2. If we get a true statement, then the boundary IS included in our graph
    1. If it makes true statement, then the boundary IS included in our graph
    1. The point (0,-2) is on our line
    2. You can choose any point on the line to test
    1. Plug 0 in for x and -2 in for y into the inequality
    1. 2(0)-2=-2
    2. It is TRUE that -2 is greater than or equal to -2
    1. It is TRUE that -2 is greater than or equal to -2
    1. So points on the line ARE included in the graph of the inequality
    1. The '≥' symbol means GREATER THAN OR EQUAL TO'
    2. The '>' symbol, without the line underneath, means GREATER THAN
    1. We'll still use (0,2), but this time we'll plug it into the inequality y>2x-2
    1. Plug 0 in for x and -2 in for y into y>2x-2
    2. Simplifying the right hand side gives us: 2(0)-2=-2
    1. Remember, '>' means GREATER THAN
    2. -2 is NOT greater than -2 - it is EQUAL TO -2!
    3. So -2>-2 is NOT a true statement
    1. Remember, '>' means GREATER THAN
    1. Remember, '≥' means GREATER THAN OR EQUAL TO