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How Do You Graph a Greater Than Inequality on the Coordinate Plane?

Graph the inequality y>2x-2

Summary

  1. '>' means 'greater than'
  2. First graph the inequality as if it were an equation
  3. We have a GREATER THAN symbol for our inequality
  4. Since we have a GREATER THAN symbol, our line will be DASHED
  5. This line is called the BOUNDARY
  6. Test the point (0,0) to see if it makes the inequality true
  7. 0 is greater than -2
  8. So we shade the half-plane that contains (0,0)

Notes

    1. We're going to pretend at first that we have an equals sign instead of an inequality sign
    1. Doing this would give us ordered pairs that we could plot in the coordinate plane
    1. This is where inequalities are different
    2. Depending on what kind of inequality symbol you have, you'll either have a DASHED line or a SOLID line
    3. A DASHED line means that points on the line are NOT included in the inequality
    4. A SOLID line means that points on the line ARE included in the inequality
    1. A DASHED line means that points on the line are NOT included in the inequality
    2. A SOLID line means that points on the line ARE included in the inequality
    1. To do this, we need to look at our inequality symbol
    2. If we have a GREATER THAN or LESS THAN symbol, our line will be DASHED
    3. If we have a GREATER THAN OR EQUAL TO or LESS THAN OR EQUAL TO symbol, our line will be SOLID
    4. The line we're drawing is called the BOUNDARY
    1. This means that the boundary is NOT a part of the inequality
    1. This means that the boundary IS a part of the inequality
    1. Our inequality is y>2x-2
    2. '>' is the symbol for GREATER THAN
    3. If it had a line underneath it, it would be a GREATER THAN OR EQUAL TO symbol
    1. This means our boundary is NOT included in our inequality
    2. So any points that fall on the line do not satisfy the inequality
    1. This means our boundary is NOT included in our inequality
    2. So any points that fall on the line do not satisfy the inequality
    1. Our boundary line splits the coordinate plane into two half-planes
    2. Only one of these half-planes contains points that make the inequality true
    3. To complete our graph, we need to figure out which half-plane that is
    1. To figure out which half-plane to shade, we are going to pick a point and plug it in to see if it makes our inequality true
    2. If it does, we know that half-plane is the solution set for our inequality
    1. If the point gives us a TRUE statement when we plug it in, then we shade in the half-plane that point is in
    2. If the point gives us a FALSE statement when we plug it in, then we shade in the OTHER half-plane
    1. Then we know that the points on that side of the boundary satisfy our inequality
    1. If we get a false statement, we know that points on that side of the boundary do NOT satisfy the inequality
    2. So that would mean that points on the other side of the boundary WOULD satisfy the inequality
    1. (0,0) is not on our boundary line, and it's really easy to work with
    2. But you could pick any point that's not on the boundary line
    1. Plug 0 in for y and x into y>2x-2
    1. 2(0)-2=-2
    2. Is 0 greater than -2?
    3. Yes it is!
    4. So we get a TRUE statement when we plug (0,0) into our inequality
    5. This means that all the points in the half-plane that contains (0,0) satisfy our inequality
    1. These points are all the possible solutions for our inequality
    2. The points in this half-plane will be our SOLUTION SET
    1. To complete our graph, all we have to do is shade the half-plane that contains our solution set
    1. The half-plane to the LEFT is the half-plane that contains (0,0)
    2. Since we know (0,0) satisfies the inequality, we know that the half-plane that contains it will be our solution