Create your own
teaching resources

Sign up for a free account to try! It takes less than 20 seconds

Create free account
Teacherbot 06 Nov, 15:31:59

Graphing Inequalities: Vocabulary and Examples

Vocabulary:

  1. Inequality: A mathematical statement that compares two quantities using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

  2. Solution: A value or set of values that make an inequality true.

  3. Graph: A visual representation of data or mathematical equations on a coordinate plane.

  4. Coordinate Plane: A two-dimensional grid formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical).

  5. x-axis: The horizontal line on a coordinate plane.

  6. y-axis: The vertical line on a coordinate plane.

  7. Open Circle: A hollow circle used to represent a value that is not included in the solution.

  8. Closed Circle: A filled-in circle used to represent a value that is included in the solution.

Examples:

  1. Graphing x < 3:
    • Draw a number line and mark a closed circle at 3.
    • Shade the line to the left of 3 to represent all values less than 3.
    • The solution is all values to the left of 3.
  2. Graphing y ≥ -2:
    • Draw a number line and mark an open circle at -2.
    • Shade the line to the right of -2 to represent all values greater than or equal to -2.
    • The solution is all values to the right of -2, including -2.
  3. Graphing x + y > 5:
    • Draw a coordinate plane with the x-axis and y-axis.
    • Rewrite the inequality in slope-intercept form: y > -x + 5.
    • Start by graphing the line y = -x + 5, which has a y-intercept of 5 and a slope of -1.
    • Since the inequality is y > -x + 5, shade the area above the line.
    • The solution is all points above the line.
  4. Graphing 2x - 3y ≤ 6:
    • Draw a coordinate plane with the x-axis and y-axis.
    • Rewrite the inequality in slope-intercept form: y ≥ (2/3)x - 2.
    • Start by graphing the line y = (2/3)x - 2, which has a y-intercept of -2 and a slope of 2/3.
    • Since the inequality is 2x - 3y ≤ 6, shade the area below the line.
    • The solution is all points below the line.

Remember to label the axes and provide a key explaining the meaning of open and closed circles. Practice graphing different inequalities to reinforce your understanding.

You 06 Nov, 15:32:43

Now I want to create 3 different versions of this. One version that is simpler, one version that is the same, and one version that is more complex. Format the output in 3 nice sections.

Teacherbot 06 Nov, 15:32:43

Version 1: Simplified

Vocabulary:

  1. Inequality: A mathematical statement that compares two quantities using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

  2. Solution: A value or set of values that make an inequality true.

  3. Graph: A visual representation of data or mathematical equations on a coordinate plane.

Examples:

  1. Graphing x < 3:
    • Draw a number line and mark a closed circle at 3.
    • Shade the line to the left of 3.
    • The solution is all values to the left of 3.
  2. Graphing y ≥ -2:
    • Draw a number line and mark an open circle at -2.
    • Shade the line to the right of -2.
    • The solution is all values to the right of -2, including -2.

Version 2: Same Difficulty

Vocabulary:

  1. Inequality: A mathematical statement that compares two quantities using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

  2. Solution: A value or set of values that make an inequality true.

  3. Graph: A visual representation of data or mathematical equations on a coordinate plane.

  4. Coordinate Plane: A two-dimensional grid formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical).

  5. x-axis: The horizontal line on a coordinate plane.

  6. y-axis: The vertical line on a coordinate plane.

  7. Open Circle: A hollow circle used to represent a value that is not included in the solution.

  8. Closed Circle: A filled-in circle used to represent a value that is included in the solution.

Examples:

  1. Graphing x < 3:
    • Draw a number line and mark a closed circle at 3.
    • Shade the line to the left of 3 to represent all values less than 3.
    • The solution is all values to the left of 3.
  2. Graphing y ≥ -2:
    • Draw a number line and mark an open circle at -2.
    • Shade the line to the right of -2 to represent all values greater than or equal to -2.
    • The solution is all values to the right of -2, including -2.
  3. Graphing x + y > 5:
    • Draw a coordinate plane with the x-axis and y-axis.
    • Rewrite the inequality in slope-intercept form: y > -x + 5.
    • Start by graphing the line y = -x + 5, which has a y-intercept of 5 and a slope of -1.
    • Shade the area above the line to represent the solution.
    • The solution is all points above the line.

Version 3: More Complex

Vocabulary:

  1. Inequality: A mathematical statement that compares two quantities using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

  2. Solution: A value or set of values that make an inequality true.

  3. Graph: A visual representation of data or mathematical equations on a coordinate plane.

  4. Coordinate Plane: A two-dimensional grid formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical).

  5. x-axis: The horizontal line on a coordinate plane.

  6. y-axis: The vertical line on a coordinate plane.

  7. Open Circle: A hollow circle used to represent a value that is not included in the solution.

  8. Closed Circle: A filled-in circle used to represent a value that is included in the solution.

Examples:

  1. Graphing x < 3:
    • Draw a number line and mark a closed circle at 3.
    • Shade the line to the left of 3 to represent all values less than 3.
    • The solution is all values to the left of 3.
  2. Graphing y ≥ -2:
    • Draw a number line and mark an open circle at -2.
    • Shade the line to the right of -2 to represent all values greater than or equal to -2.
    • The solution is all values to the right of -2, including -2.
  3. Graphing x + y > 5:
    • Draw a coordinate plane with the x-axis and y-axis.
    • Rewrite the inequality in slope-intercept form: y > -x + 5.
    • Start by graphing the line y = -x + 5, which has a y-intercept of 5 and a slope of -1.
    • Shade the area above the line to represent the solution.
    • The solution is all points above the line.
  4. Graphing 2x - 3y ≤ 6:
    • Draw a coordinate plane with the x-axis and y-axis.
    • Rewrite the inequality in slope-intercept form: y ≥ (2/3)x - 2.
    • Start by graphing the line y = (2/3)x - 2, which has a y-intercept of -2 and a slope of 2/3.
    • Shade the area below the line to represent the solution.
    • The solution is all points below the line.

Remember to label the axes and provide a key explaining the meaning of open and closed circles. Practice graphing different inequalities to reinforce your understanding.