Answer:
To graph the inequality y > -2x - 5, we can start by graphing the corresponding equation y = -2x - 5.
Explanation:
Step 1: Plot the y-intercept
The y-intercept is the point where the line intersects the y-axis. In this case, the y-intercept is -5. So, plot the point (0, -5) on the graph.
Step 2: Determine the slope
The slope of the line is -2. This means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2. Using the slope, find another point on the line.
One way to do this is to use the rise-over-run method. Start from the y-intercept (0, -5) and move down 2 units (rise) and to the right 1 unit (run). This gives us the point (1, -7). Plot this point on the graph.
Step 3: Draw the line
Now, draw a straight line passing through the two points you plotted. This line represents the equation y = -2x - 5.
Step 4: Shade the region above the line
Since the inequality is y > -2x - 5, we need to shade the region above the line. This means that any point above the line will satisfy the inequality. You can shade the region above the line or draw arrows pointing upwards to indicate this.
Note: If the inequality had been y < -2x - 5, we would shade the region below the line instead.
To summarize, graph the equation y = -2x - 5 and shade the region above the line to represent the inequality y > -2x - 5.
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