Final answer:
A dashed line in the context of the inequality 5x + 3y > 9 represents a boundary for the graphical solution that is not included in the set of solutions because the inequality is strict. A solid line would signify that the boundary is included in the set of solutions. The slope and y-intercept determine the position of the line on the graph.
Step-by-step explanation:
In the context of the inequality 5x + 3y > 9, the concepts of a dashed line and a solid line represent different types of boundary conditions on a graph. A solid line typically denotes that the points on the line satisfy the equation, while a dashed line implies that the points on the line do not satisfy the inequality. In this case, since we have a strict inequality (greater than, not greater than or equal to), we would use a dashed line to represent the boundary on a graph. This line would be the graph of the equation 5x + 3y = 9 if it were an equality.
When graphing the inequality, one would find the y-intercept, which is 9 in this case, and use the slope, which is 3 (rise over run), to determine the direction and steepness of the line. The dashed line helps to indicate which side of the line the inequality represents, with the region above the dashed line (where 5x + 3y values are greater than 9) being the solution to the inequality. The dashed line itself, however, is not part of the solution since the inequality does not include the equals sign (> rather than ≥).