Question

graph the inequality in the coordinate plane.
$x \leq -2$

Explanation:

Step 1: Identify the type of line

The inequality is \( x \leq -2 \). For vertical lines of the form \( x = a \), when the inequality is \( \leq \) or \( \geq \), we use a solid line (to include the boundary). So we draw a solid vertical line at \( x = -2 \) (where the \( x \)-coordinate is always -2, and \( y \) can be any real number).

Step 2: Determine the shaded region

Since \( x \leq -2 \), we want all points where the \( x \)-value is less than or equal to -2. On the coordinate plane, this is the region to the left of the line \( x = -2 \). So we shade the area to the left of the solid vertical line at \( x = -2 \).

Answer:

To graph \( x \leq -2 \):

1. Draw a vertical line at \( x = -2 \) (since \( x \) is constant, it's a vertical line). The line should be solid because the inequality is "less than or equal to" (so points on the line are included).
2. Shade the region to the left of the line \( x = -2 \), because we want all \( x \)-values that are less than or equal to \( -2 \).