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.
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Line A: \( y = 2x - 3 \)
- Slope: \( m_A = 2 \)
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Line B: \( y = 2x + 5 \)
- Slope: \( m_B = 2 \)
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Line C: \( y = -12x - 2 \)
- Slope: \( m_C = -12 \)
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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.
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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.