Question

Which statements are true about y≤8 and its graph? Check the four that apply.(4 points)Responsesy=8 is part of the solution set.y is equal to 8 is part of the solution set.y=0 is part of the solution set.y is equal to 0 is part of the solution set.There is an open circle on the graph at 8.There is an open circle on the graph at 8.The arrow on the graph points left.The arrow on the graph points left.The arrow on the graph points right.The arrow on the graph points right.There is a closed circle on the graph at 8.There is a closed circle on the graph at 8.y=10 is part of the solution set.

Answer 1

To evaluate the statements regarding the inequality \( y \leq 8 \) and its graph, let's break it down:

1. y = 8 is part of the solution set.

   • True. Since the inequality is \( \leq \), the values of \( y \) can equal 8.

2. y is equal to 8 is part of the solution set.

   • True. This is the same statement as the first one, just phrased differently.

3. y = 0 is part of the solution set.

   • True. Since 0 is less than 8, it satisfies the inequality.

4. y is equal to 0 is part of the solution set.

   • True. This is the same as the previous statement, just phrased differently.

5. There is an open circle on the graph at 8.

   • False. The graph includes the value \( y = 8 \), so it will be shown with a closed circle.

6. The arrow on the graph points left.

   • False. The inequality \( y \leq 8 \) will be represented by a horizontal line (not pointing left or right).

7. The arrow on the graph points right.

   • False. Again, the graph is a horizontal line of solutions.

8. There is a closed circle on the graph at 8.

   • True. Since \( y \) can equal 8, it will have a closed circle at this point.

9. y = 10 is part of the solution set.

   • False. Since 10 is greater than 8, it does not satisfy the inequality.

True Statements:

1. y = 8 is part of the solution set.
2. y is equal to 8 is part of the solution set.
3. y = 0 is part of the solution set.
4. y is equal to 0 is part of the solution set.
5. There is a closed circle on the graph at 8.

So the correct true statements are: 1, 2, 3, 4, and 8.