Question

Sketch the graph of the inequality. $$y>-3$$

Short answer

The graph for the inequality \(y > -3\) is a shaded region above the dashed horizontal line \(y = -3\).

Step-by-step solution

Understand the basic concept

At first, it is important to understand that the inequality \(y > -3\) means that the value of 'y' is greater than -3. Therefore, on a 2D plane (graph), this would represent all the points where the y-coordinate is greater than -3.

Draw a horizontal line

For visualization, it is easier to first draw a horizontal line at \(y = -3\). This line serves as a demarcation line separating the graph into two parts.

Utilize shading

To indicate the solution to the inequality, we need to shade the area of the graph representing the condition \(y > -3\), which is the area above the line we drew at Step 2.

Exclusion of the line y=-3

Since the inequality is strict (i.e., y is strictly greater than -3 rather than greater than or equal to -3), the line \(y = -3\) should not be included in the solution. This is usually represented by drawing said line as a dashed line.