Final answer:
The graph of the inequality 2x - 5y < 6 is represented by a dashed line, since the inequality is strict, and the region below the line is shaded, as this side contains the origin (0,0), which satisfies the inequality.
Step-by-step explanation:
The inequality 2x - 5y < 6 represents a region in the coordinate plane. To graph this inequality, we first graph the boundary line, which comes from the corresponding equation 2x - 5y = 6. Because the inequality is strictly less than (<), not less than or equal to (\u2264), the boundary line is drawn as a dashed line, indicating that points on the line itself are not included in the solution set.
Next, to determine which side of the line to shade, we can test a point not on the line, such as the origin (0,0). Substituting (0,0) into the inequality 2(0) - 5(0) < 6 gives 0 < 6, which is true. This means that the region containing the origin is part of the solution set, so we shade that side of the line.
Since the coefficient of y is negative in the inequality (which means the slope of the boundary line is positive when solved for y), the line slopes upward to the right. So, the correct description of the graph of the inequality 2x - 5y < 6 is D. Dashed and shaded below the line.