The graph of the inequality y≥−x−1 is graph 4 (y\ge-x-1) . Therefore , graph 4 (y\ge-x-1) is correct .
The graph of (y\ge-x-1) is a half-plane above the line (y=-x-1), which is shown in the image.
The line (y=-x-1) has a slope of -1 and a y-intercept of -1.
To identify the graph of (y\ge-x-1), we can start by plotting the line (y=-x-1). Then, we can shade in the half-plane above the line.
Here is a detailed explanation of how to plot the graph of (y\ge-x-1):
Plot the line (y=-x-1). To do this, we need to find two points on the line. We can start by finding the y-intercept, which is -1.
This means that the line must pass through the point (0, -1).
Next, we can use the slope of the line to find another point on the line.
The slope of the line is -1, which means that for every 1 unit we move down on the y-axis, we must also move 1 unit to the right on the x-axis.
So, if we start at the point (0, -1) and move 1 unit to the right and 1 unit down, we will arrive at the point (1, -2).
Now that we have two points on the line, we can connect them with a straight line.
The line should pass through the points (0, -1) and (1, -2).
Shade in the half-plane above the line. The graph of (y\ge-x-1) is the half-plane above the line (y=-x-1).
This means that we need to shade in the region above the line.
To do this, we can use a different color to shade in the region above the line.
For example, we could use blue to shade in the region above the line.
The blue region is the graph of (y\ge-x-1).