Question
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.
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.
and its graph? Check the four that apply.(4 points)
Responses
y=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.
Answers
Answered by
GPT-4o mini
To analyze the inequality \( y \leq 8 \) and its graph, let's go through the statements one by one:
1. **y=8 is part of the solution set.**
**True**. The inequality \( y \leq 8 \) includes the value \( y = 8 \) itself, as the inequality is "less than or equal to."
2. **There is a closed circle on the graph at 8.**
**True**. When graphing \( y \leq 8 \), a closed circle is used at \( y = 8 \) because that value is included in the solution set.
3. **The arrow on the graph points left.**
**False**. For the inequality \( y \leq 8 \), the graph is not a horizontal line; rather, it represents all points below \( y = 8 \).
4. **The arrow on the graph points right.**
**False**. Similar to the above, the graph will only extend downward (or vertically).
5. **y=0 is part of the solution set.**
**True**. Since \( 0 \) is less than \( 8 \), it satisfies the inequality \( y \leq 8 \).
6. **There is an open circle on the graph at 8.**
**False**. In this case, as discussed, there is a closed circle at \( y = 8 \).
7. **y=10 is part of the solution set.**
**False**. The value \( 10 \) does not satisfy \( y \leq 8 \), so it is not part of the solution set.
Based on this analysis, the true statements about the inequality \( y \leq 8 \) are:
1. y=8 is part of the solution set.
2. There is a closed circle on the graph at 8.
3. y=0 is part of the solution set.
1. **y=8 is part of the solution set.**
**True**. The inequality \( y \leq 8 \) includes the value \( y = 8 \) itself, as the inequality is "less than or equal to."
2. **There is a closed circle on the graph at 8.**
**True**. When graphing \( y \leq 8 \), a closed circle is used at \( y = 8 \) because that value is included in the solution set.
3. **The arrow on the graph points left.**
**False**. For the inequality \( y \leq 8 \), the graph is not a horizontal line; rather, it represents all points below \( y = 8 \).
4. **The arrow on the graph points right.**
**False**. Similar to the above, the graph will only extend downward (or vertically).
5. **y=0 is part of the solution set.**
**True**. Since \( 0 \) is less than \( 8 \), it satisfies the inequality \( y \leq 8 \).
6. **There is an open circle on the graph at 8.**
**False**. In this case, as discussed, there is a closed circle at \( y = 8 \).
7. **y=10 is part of the solution set.**
**False**. The value \( 10 \) does not satisfy \( y \leq 8 \), so it is not part of the solution set.
Based on this analysis, the true statements about the inequality \( y \leq 8 \) are:
1. y=8 is part of the solution set.
2. There is a closed circle on the graph at 8.
3. y=0 is part of the solution set.