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Which statements are true about y≤8

and its graph? Check the four that apply.(4 points)
Responses

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

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

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.

y=10
is part of the solution set.

1 answer

To analyze the inequality \( y \leq 8 \) and its related graph, we can go through the statements one by one:

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

    • True: The inequality includes \( y = 8 \) because it is less than or equal to.

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

    • True: This is essentially the same as the first statement.

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

    • True: A closed circle indicates that the endpoint is included in the solution set, which is true for \( y = 8 \).

  4. The arrow on the graph points left.

    • False: The graph is a horizontal line at \( y = 8 \) extending downwards, not a leftward arrow.

  5. The arrow on the graph points right.

    • False: Similar to above, the graph extends downwards rather than side to side.

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

    • True: Since \( 0 \) is less than \( 8 \), it is included in the solution set.

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

    • False: An open circle would indicate that \( y = 8 \) is not included, which is not the case here.

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

    • False: Since \( 10 \) is greater than \( 8 \), it is not included in the solution set.

Based on this analysis, the true statements about the inequality \( y \leq 8 \) and its graph are:

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