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A coordinate plane, or Cartesian grid, is a two-dimensional surface for graphing mathematical equations and inequalities. It is divided into four quadrants by two axes: the x-axis, which runs horizontally, and the y-axis, which runs vertically. The point where these axes intersect is called the origin, indicated by the ordered pair (0,0).
Understanding how to navigate the coordinate plane is essential for graphing inequalities. Each point on the plane is defined by an ordered pair (x, y), where 'x' is the horizontal position and 'y' is the vertical position.

• Quadrant I: Both x and y values are positive.
• Quadrant II: x is negative, but y is positive.
• Quadrant III: Both x and y are negative.
• Quadrant IV: x is positive, but y is negative.

When graphing an inequality like \(y > -3\), you will work within this framework to plot the relevant horizontal line and determine which parts of the plane should be shaded.

Linear inequalities, such as \(y > -3\), express a relationship where one side is greater than or less than the other. Unlike equations, which have solutions that are precise points, inequalities have a range of solutions that often form a region on the coordinate plane.
To graph the inequality \(y > -3\), follow these steps:

• First, consider the related equation \(y = -3\), which is a horizontal line. This forms the boundary of the inequality.
• Because the inequality is strict (greater than and not greater than or equal to), the line must be dashed. This indicates that points on the line itself are not included in the solution set.

Linear inequalities divide the coordinate plane into two regions. The solution set for the inequality is one of these regions. Understanding which region to focus on involves analyzing where the inequality holds true.

Shading is a crucial step in graphing inequalities. It visually represents the set of possible solutions to the inequality on the coordinate plane. The direction of shading is determined by the inequality's nature—greater than or less than.
For the inequality \(y > -3\):

• You draw a horizontal dashed line along \(y = -3\) to represent the boundary.
• Since the inequality is \(y > -3\), shade the region above the line. This covers all y-values larger than -3.

These shaded regions show where the inequality holds true. In practice, pick a test point not on the dashed line to confirm the correct region. A common choice is the origin, (0,0), unless it lies on the dashed line. Substitute this point into the inequality to ensure its validity within that region. The shading provides a clear and effective way to communicate the solutions visually.