Question

Sketch the graph of the inequality in a coordinate plane. $$ y \leq-1.5 $$

Short answer

The graph includes a line on \(y = -1.5\) and shading below the line, indicating all the points where \(y \leq -1.5\).

Step-by-step solution

Understand the inequality

The inequality \(y \leq -1.5\) means that we want to find all the (x,y) pairs such that the y-coordinate is less than or equal to -1.5. This corresponds to a horizontal line along the y = -1.5 and all the area below it.

Draw the line

Next, draw a horizontal line on your coordinate plane at where y equals -1.5. This line includes every x-coordinate because we don't have restrictions on x in our inequality.

Shade the area below

The inequality specifies \(y \leq -1.5\), meaning the line and the area below it (where y is less than -1.5) should be shaded to indicate the solution area.