Final answer:
To graph the inequality y < -3/4x - 4, graph the line y = -3/4x - 4 with a dashed line to indicate it is not included in the solution set. Then, shade the region below the line to represent the inequality solution. Therefore, the correct answer to the question would be: a) Shaded region below the line.
Step-by-step explanation:
To graph the inequality y < -3/4x - 4, you should start by graphing the line y = -3/4x - 4. This equation represents a straight line with a negative slope. According to the figure `Figure 12.4` descriptions given in the question, if b < 0, the line slopes downward to the right, which is consistent with our equation since our slope (b) is -3/4.
The best solution to the inequality y < -3/4x - 4 is represented by the graph in option b) Shaded region above the line.
To graph the inequality, we start by plotting the line y = -3/4x - 4. Since the inequality is y < -3/4x - 4, we need to shade the region above the line since the line itself is not included in the solution set.
The graph would show a straight line with a negative slope, and the shaded region would be above the line.
Once you have graphed the line, to represent the inequality y < -3/4x - 4, you would typically use a dashed line to indicate that the line itself is not included in the solution set (since this is a '<' rather than a '≤' inequality). Finally, because the inequality is '<' (less than), you would shade the region below the line. This shows all the points (x,y) that satisfy the inequality y is less than -3/4x - 4.
Therefore, the correct answer to the question would be: a) Shaded region below the line.