Final answer:
To graph the linear inequality Y ≤ 7/3 x - 2, sketch the line y = 7/3 x - 2 by plotting the y-intercept and using the slope to find another point, then shade below the line to represent the inequality.
Step-by-step explanation:
To sketch the graph of the linear inequality Y ≤ 7/3 x - 2, you need to follow these steps:
- First, sketch the line y = 7/3 x - 2. This is the boundary of the inequality. Start by plotting the y-intercept, which is (0,-2). Next, use the slope, which is 7/3, to identify another point. From the y-intercept, move up 7 units and right 3 units to get to the next point on the line.
- Once the line is drawn, determine which side of the line to shade. Since the inequality is ≤ (less than or equal to), you will shade the area below the line, representing all the points where y is less than or equal to the boundary line.
By shading the correct side, you indicate that all points in that area satisfy the inequality Y ≤ 7/3 x - 2.