The y < 2/3x - 1 is the linear inequality represented by the graph.
Analyzing the provided options:
y > 2/3x - 2: This inequality represents a line with a slope greater than 2/3 and a y-intercept of -2. By plotting this line, we can see that it lies below the given shaded area, making it incorrect.
y < 2/3x + 2: This inequality represents a line with a slope less than 2/3 and a y-intercept of 2. By plotting this line, we can see that it lies above the shaded area, making it incorrect.
y > 2/3x + 1: This inequality represents a line with a slope greater than 2/3 and a y-intercept of 1. By plotting this line, we can see that it intersects the shaded area, making it incorrect.
y < 2/3x - 1: This inequality represents a line with a slope less than 2/3 and a y-intercept of -1. By plotting this line, we can see that it lies entirely below the shaded area, making it the correct answer.
Therefore, y < 2/3x - 1 is the linear inequality represented by the graph.