Question
Use the table to answer the question. Line Equation Line A y=2x−3 Line B y=2x+5 Line C y=−12x−2 Line D y=12x+2 Given the linear equations in the table, which of the following statements is true? (1 point) Responses Line B is perpendicular to line D . Line upper B is perpendicular to line upper D . Line C is perpendicular to line D . Line upper C is perpendicular to line upper D . Line A is perpendicular to line C . Line upper A is perpendicular to line upper C . Line A is perpendicular to line B .
Select One
Select One
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which lines are perpendicular, we need to look at the slopes of each line. The general form of a linear equation is \( y = mx + b \), where \( m \) represents the slope.
1. **Line A:** \( y = 2x - 3 \)
- Slope: \( m_A = 2 \)
2. **Line B:** \( y = 2x + 5 \)
- Slope: \( m_B = 2 \)
3. **Line C:** \( y = -12x - 2 \)
- Slope: \( m_C = -12 \)
4. **Line D:** \( y = 12x + 2 \)
- Slope: \( m_D = 12 \)
Lines are perpendicular if the product of their slopes is -1. Therefore, we will look for pairs of slopes that satisfy this condition.
- For **Line A** and **Line B**:
\( 2 \times 2 = 4 \) (Not perpendicular)
- For **Line A** and **Line C**:
\( 2 \times -12 = -24 \) (Not perpendicular)
- For **Line A** and **Line D**:
\( 2 \times 12 = 24 \) (Not perpendicular)
- For **Line B** and **Line C**:
\( 2 \times -12 = -24 \) (Not perpendicular)
- For **Line B** and **Line D**:
\( 2 \times 12 = 24 \) (Not perpendicular)
- For **Line C** and **Line D**:
\( -12 \times 12 = -144 \) (Not perpendicular)
The only way for two lines to be perpendicular is if their slopes are negative reciprocals of each other. In this case, the slopes of lines A and D are not negative reciprocals, and neither are any others.
From the analysis, none of the lines in the table are perpendicular to each other.
None of the provided statements ("Line B is perpendicular to line D", "Line C is perpendicular to line D", "Line A is perpendicular to line C", or "Line A is perpendicular to line B") are true.
However, if we strictly have to choose a true statement based on the results, you can state that none of the provided options are correct.
1. **Line A:** \( y = 2x - 3 \)
- Slope: \( m_A = 2 \)
2. **Line B:** \( y = 2x + 5 \)
- Slope: \( m_B = 2 \)
3. **Line C:** \( y = -12x - 2 \)
- Slope: \( m_C = -12 \)
4. **Line D:** \( y = 12x + 2 \)
- Slope: \( m_D = 12 \)
Lines are perpendicular if the product of their slopes is -1. Therefore, we will look for pairs of slopes that satisfy this condition.
- For **Line A** and **Line B**:
\( 2 \times 2 = 4 \) (Not perpendicular)
- For **Line A** and **Line C**:
\( 2 \times -12 = -24 \) (Not perpendicular)
- For **Line A** and **Line D**:
\( 2 \times 12 = 24 \) (Not perpendicular)
- For **Line B** and **Line C**:
\( 2 \times -12 = -24 \) (Not perpendicular)
- For **Line B** and **Line D**:
\( 2 \times 12 = 24 \) (Not perpendicular)
- For **Line C** and **Line D**:
\( -12 \times 12 = -144 \) (Not perpendicular)
The only way for two lines to be perpendicular is if their slopes are negative reciprocals of each other. In this case, the slopes of lines A and D are not negative reciprocals, and neither are any others.
From the analysis, none of the lines in the table are perpendicular to each other.
None of the provided statements ("Line B is perpendicular to line D", "Line C is perpendicular to line D", "Line A is perpendicular to line C", or "Line A is perpendicular to line B") are true.
However, if we strictly have to choose a true statement based on the results, you can state that none of the provided options are correct.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.