Projects on How to Graph Inequalities

Inequalities are equations in which the relationship between the two sides are less-than signs, "<," or greater-than signs, ">," instead of an equal sign. This means the solution to the equation includes a range of values and not just one value. For example, if the solution to an equation is x = 3, then the only solution is 3. However, if the solution is an inequality such as x > 3, then the solution is all of the values greater than 3, which is an infinite number of values. You can also have a less than and equal to inequality, "<=," or a greater than and equal to inequality, ">=," which is just a combination of the two options.
  1. Graph y > 3x + 2

    • Convert the inequality sign into an equal sign: y = 3x + 2. Graph the equation by drawing an x-y graph and label both the x-y axis from 1 to 10. Label both axis in the positive and negative direction. At x = 1, y = 5. Plot the point (1, 5). At x = 2, y = 8. Plot the point (2, 8). Plot two negative numbers to complete the graph. At x = -1, y is -1. Plot the point (-1, -1). At x = -2, y = -4. Plot the point (-2, -4). Connect the points into a line. Shade in the inequality on the graph. Since the inequality is a greater than sign, the inequality is true for all y values greater than the line. Therefore, you shade all of the area of the graph that is north of the line because north of the line represents all values where y is greater than the line. Be sure the shade does not touch the line because touching the line will mean "equal to."

    Graph y < 4x - 6

    • Convert the inequality sign into an equal sign: y = 4x - 6. Graph the equation by drawing out an x-y graph and label both the x-y axis from 1 to 10. Label both axis in the positive and negative direction. At x = 1, y = -2. Plot the point (1,-2). At x = 2, y = 2. Plot the point (2, -2). Plot two negative numbers to complete the graph. At x = -1, y is -10. Plot the point (-1, -10). At x = -2, y = -14. Plot the point (-2, -14). Connect the points into a line. Shade in the inequality on the graph. Since the inequality is a less than the sign, the inequality is true for all y values less than the line. Therefore, shade all of the area of the graph that is south of the line because south of the line represents all values where y is less than the line. Be sure the shade does not touch the line because touching the line will mean "equal to."

    Graph y >= 2x + 4

    • Convert the inequality sign into an equal sign: y = 2x + 4. Graph the equation drawing out an x-y graph and label both the x-y axis from 1 to 10. Label both axis in the positive and negative direction. At x = 1, y = 6. Plot the point (1, 6). At x = 2, y = 8. Plot the point (2, 8). Plot two negative numbers to complete the graph. At x = -1, y is 2. Plot the point (-1, 2). At x = -2, y = 0. Plot the point (-2, 0). Connect the points into a line. Shade in the inequality on the graph. Since the inequality is a greater than and equal to sign, the inequality is true for all y values equal to and greater than the line. Therefore, shade the line and all of the area of the graph that is north of the line because north of the line represents all values where y is greater than the line.

    Graph y <= 2x - 3

    • Convert the inequality sign into an equal sign: y = 2x - 3. Graph the equation by drawing out an x-y graph and label both the x-y axis from 1 to 10. Label both axis in the positive and negative direction. At x = 1, y = -1. Plot the point (1,-1). At x = 2, y = 1. Plot the point (2, 1). Plot two negative numbers to complete the graph. At x = -1, y is -5. Plot the point (-1, -5). At x = -2, y = -7. Plot the point (-2, -7). Connect the points into a line. Shade in the inequality on the graph. Since the inequality is a less than and equal to sign, the inequality is true for all y values equal to and less than the line. Therefore, shade the line and all of the area of the graph that is south of the line because south of the line represents all values where y is less than the line.

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