Start with the example y < 3x + 4. As you can see, the "x" term has an exponent of 1 or it's to the power of one. If you plot this inequality, you will get a straight line as a boundary on an x-y plot and shade in the area where "y" is less than the line or the area of the graph below the line in the downward y-direction. Another example of a first-degree inequality is y > 4x - 6. This is a greater-than sign where the solution will be a shaded graph above the line in the upward y-direction.
First-degree inequalities come into focus when comparing one to a second-degree inequality. An example of a second-degree inequality is y < x^2 + 6 where the "x" term is to the second power. Also, second-order equations are not straight lines. They are exponential or parabola-shaped curves. Similar to first-degree inequalities, however, you graph them by shading in the areas above or below the curves or shapes, depending on whether the inequality is a less-than or greater-than.
As noted previously, the solution for inequalities comes in the form of a graph. To prepare for the graph, you have to calculate or compute points. To do this, first you change the equality to an "=" sign and then solve the equation for y at various values of x. For example, the inequality y < 3x + 4 changes to y = 3x + 4. Now, calculate the (x, y) points. At x = 1, y = 7. Plot the (x, y) point (1,7). At x = 2, y = 10. Plot the point (2, 10). Try a few negative numbers. At x = -1, y is 1. Plot the point (-1, 1). At x = -2, y = -2. Plot the point (-2, -2).
To the graph equation, simply connect the x-y points with a line. This line is the boundary of the solution. Next, identify the inequality on the graph. With the equation y < 3x + 4, "y" is before a less-than sign, which means the inequality is true for all y-values less than the line. Shade all of the area of the graph that is south of the line because south or in the downward direction represent "y" less than the line.