Final answer:
The graph representing the inequality y > 3 - x is a dashed downward sloping line with a y-intercept of 3, with the region above the line shaded to indicate all the solutions to the inequality.
Step-by-step explanation:
To determine which graph represents the inequality y > 3 - x, it is helpful to first understand the graph of the equation y = 3 - x. This is a linear equation with a slope (b) of -1 (since the coefficient of x is -1) and a y-intercept (a) of 3. Referencing the information given, if b < 0, the line slopes downward to the right as seen in Figure 12.4 (c).
The inequality y > 3 - x means that we are looking for the region above this line. To represent this graphically, one would draw the line y = 3 - x and then shade the area above it since the inequality is greater than. Importantly, the line itself would be dashed to indicate that it is not included in the solution set (since the inequality is strictly greater than, not greater than or equal to).
In summary, you would sketch a dashed line that decreases from left to right with a y-intercept of 3, and then shade the entire region above that line to represent the inequality y > 3 - x.