Final Answer:
The correct inequality for describing the shaded region of the graph is b) y < 2x - 3
Step-by-step explanation:
The correct inequality for describing the shaded region of the graph is b) y < 2x - 3 (Option b). To understand why, let's examine the inequality in relation to the graph.
1. **Graphical Interpretation:** The inequality y < 2x - 3 represents a shaded region below the line y = 2x - 3 on the coordinate plane. This is because any point (x, y) below the line will satisfy the inequality, while points above the line will not.
2. **Slope-Intercept Form:** The inequality can be rewritten in the slope-intercept form y = mx + b where m is the slope and b is the y-intercept. In this case, the line has a slope of 2 and a y-intercept of -3, indicating that it rises at a steeper rate than a 45-degree angle from the x-axis.
3. **Comparison to Options:** Options a, c, and d present variations of the inequality, but the correct choice is y < 2x - 3 (Option b) as it accurately represents the region below the line on the graph.
In summary, the correct inequality y < 2x - 3 characterizes the shaded region below the line on the graph. Understanding the slope and y-intercept helps interpret the relationship between the inequality and the graphical representation, leading to the selection of the accurate option.