Question

Sketch the graph of the inequality. $$y \geq 1.5$$

Short answer

The graph of the inequality \(y \geq 1.5\) is a line at \(y=1.5\) on the Cartesian plane, with the area above, and including, the line shaded. This shaded area represents where \(y\) is greater than or equal to 1.5.

Step-by-step solution

Identify the inequality

In this equation, there is a greater than or equal to inequality involving the y-variable. This type of inequality describes a line and a specific region of the Cartesian plane that it encompasses. Here, \(y \geq 1.5\)

Draw the line

The line represented by this inequality is a horizontal line at \(y = 1.5\). This means, the line passes through all points whose y-coordinate is 1.5.

Shade the area

Since the inequality is \(y \geq 1.5\), this means that all points within the region where the y-coordinate is greater than or equal to 1.5 are included. Therefore, the area above the line, including the line itself, should be shaded to represent the solution set of this inequality.