Answer :
To determine which points are solutions to the inequality \( y < 0.5x + 27 \), we'll evaluate each point individually against the inequality.
1. Evaluating \((-3, -2)\):
- Substitute \( x = -3 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-3) + 27 = -1.5 + 27 = 25.5 \][/tex]
- Now, compare \( y = -2 \) with 25.5:
[tex]\[ -2 < 25.5 \quad \text{(True)} \][/tex]
- So, \((-3, -2)\) is a solution.
2. Evaluating \((-2, 1)\):
- Substitute \( x = -2 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-2) + 27 = -1 + 27 = 26 \][/tex]
- Now, compare \( y = 1 \) with 26:
[tex]\[ 1 < 26 \quad \text{(True)} \][/tex]
- So, \((-2, 1)\) is a solution.
3. Evaluating \((-1, -2)\):
- Substitute \( x = -1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-1) + 27 = -0.5 + 27 = 26.5 \][/tex]
- Now, compare \( y = -2 \) with 26.5:
[tex]\[ -2 < 26.5 \quad \text{(True)} \][/tex]
- So, \((-1, -2)\) is a solution.
4. Evaluating \((-1, 2)\):
- Substitute \( x = -1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-1) + 27 = -0.5 + 27 = 26.5 \][/tex]
- Now, compare \( y = 2 \) with 26.5:
[tex]\[ 2 < 26.5 \quad \text{(True)} \][/tex]
- So, \((-1, 2)\) is a solution.
5. Evaluating \((1, -2)\):
- Substitute \( x = 1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(1) + 27 = 0.5 + 27 = 27.5 \][/tex]
- Now, compare \( y = -2 \) with 27.5:
[tex]\[ -2 < 27.5 \quad \text{(True)} \][/tex]
- So, \((1, -2)\) is a solution.
Given this evaluation, the three points that are solutions to the inequality \( y < 0.5x + 27 \) are:
- \((-3, -2)\)
- \((-2, 1)\)
- \((-1, -2)\)
- \((-1, 2)\)
- \((1, -2)\)
As per the requirement to select three options, you can choose any three out of these. For instance, a possible selection is:
- \((-3, -2)\)
- \((-2, 1)\)
- [tex]\((-1, -2)\)[/tex]
1. Evaluating \((-3, -2)\):
- Substitute \( x = -3 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-3) + 27 = -1.5 + 27 = 25.5 \][/tex]
- Now, compare \( y = -2 \) with 25.5:
[tex]\[ -2 < 25.5 \quad \text{(True)} \][/tex]
- So, \((-3, -2)\) is a solution.
2. Evaluating \((-2, 1)\):
- Substitute \( x = -2 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-2) + 27 = -1 + 27 = 26 \][/tex]
- Now, compare \( y = 1 \) with 26:
[tex]\[ 1 < 26 \quad \text{(True)} \][/tex]
- So, \((-2, 1)\) is a solution.
3. Evaluating \((-1, -2)\):
- Substitute \( x = -1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-1) + 27 = -0.5 + 27 = 26.5 \][/tex]
- Now, compare \( y = -2 \) with 26.5:
[tex]\[ -2 < 26.5 \quad \text{(True)} \][/tex]
- So, \((-1, -2)\) is a solution.
4. Evaluating \((-1, 2)\):
- Substitute \( x = -1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(-1) + 27 = -0.5 + 27 = 26.5 \][/tex]
- Now, compare \( y = 2 \) with 26.5:
[tex]\[ 2 < 26.5 \quad \text{(True)} \][/tex]
- So, \((-1, 2)\) is a solution.
5. Evaluating \((1, -2)\):
- Substitute \( x = 1 \) into the equation \( y = 0.5x + 27 \):
[tex]\[ y = 0.5(1) + 27 = 0.5 + 27 = 27.5 \][/tex]
- Now, compare \( y = -2 \) with 27.5:
[tex]\[ -2 < 27.5 \quad \text{(True)} \][/tex]
- So, \((1, -2)\) is a solution.
Given this evaluation, the three points that are solutions to the inequality \( y < 0.5x + 27 \) are:
- \((-3, -2)\)
- \((-2, 1)\)
- \((-1, -2)\)
- \((-1, 2)\)
- \((1, -2)\)
As per the requirement to select three options, you can choose any three out of these. For instance, a possible selection is:
- \((-3, -2)\)
- \((-2, 1)\)
- [tex]\((-1, -2)\)[/tex]
