Questions: Graph the inequality. y ≤ -1/2 x - 1

Solution Steps

The inequality given is \( y \leq -\frac{1}{2}x - 1 \). This is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = -1 \).

Plot the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis. For \( b = -1 \), plot the point (0, -1).

The slope \( m = -\frac{1}{2} \) means that for every 2 units you move to the right on the x-axis, you move 1 unit down on the y-axis. Starting from the y-intercept (0, -1), move 2 units to the right to (2, -1) and then 1 unit down to (2, -2). Plot this point (2, -2).

Draw a straight line through the points (0, -1) and (2, -2). Since the inequality is \( \leq \), the line should be solid, indicating that points on the line satisfy the inequality.

Since the inequality is \( y \leq -\frac{1}{2}x - 1 \), shade the region below the line. This represents all the points where \( y \) is less than or equal to \( -\frac{1}{2}x - 1 \).

Final Answer