Answer:
In summary, the graph that shows the solutions for the linear inequality y > -1/3x + 1 is a dotted line with a negative slope of -1/3 passing through the points (0, 1) and (3, 0), and the region above the line (excluding the line) shaded to represent the solutions.
Explanation:
The graph that represents the solutions for the linear inequality y > -1/3x + 1 is a dotted line that goes through the point (0, 1) and has a negative slope of -1/3. The region above this line, excluding the line itself, represents the solutions.
To graph the inequality, we can start by plotting the y-intercept, which is (0, 1). From there, we can use the slope of -1/3 to find additional points. Since the slope is negative, we can move three units to the right and one unit down from the y-intercept to find another point, which is (3, 0).
Now, we can draw a dotted line passing through these two points. The line should be dotted to represent that the inequality is "greater than" and not "greater than or equal to."
Finally, we shade the region above the line, excluding the line itself, to represent the solutions. This is because any point above the line would satisfy the inequality y > -1/3x + 1.