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 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 B is perpendicular to line D . Line upper B is perpendicular to line upper D . Line A is perpendicular to line B . Line upper A is perpendicular to line upper B . Skip to navigation

Answer 1

To determine which lines are perpendicular to each other, we need to look at the slopes of the lines given in the equations.

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope.

• Line A: \(y = 2x - 3\) → slope \(m_A = 2\)
• Line B: \(y = 2x + 5\) → slope \(m_B = 2\)
• Line C: \(y = -12x - 2\) → slope \(m_C = -12\)
• Line D: \(y = 12x + 2\) → slope \(m_D = 12\)

Two lines are perpendicular if the product of their slopes is \(-1\).

Now, let's check the slopes:

1. Line A and Line B:

   • \(m_A = 2\) and \(m_B = 2\)
   • \(m_A \cdot m_B = 2 \cdot 2 = 4\) (not perpendicular)

2. Line A and Line C:

   • \(m_A = 2\) and \(m_C = -12\)
   • \(m_A \cdot m_C = 2 \cdot (-12) = -24\) (not perpendicular)

3. Line A and Line D:

   • \(m_A = 2\) and \(m_D = 12\)
   • \(m_A \cdot m_D = 2 \cdot 12 = 24\) (not perpendicular)

4. Line B and Line C:

   • \(m_B = 2\) and \(m_C = -12\)
   • \(m_B \cdot m_C = 2 \cdot (-12) = -24\) (not perpendicular)

5. Line B and Line D:

   • \(m_B = 2\) and \(m_D = 12\)
   • \(m_B \cdot m_D = 2 \cdot 12 = 24\) (not perpendicular)

6. Line C and Line D:

   • \(m_C = -12\) and \(m_D = 12\)
   • \(m_C \cdot m_D = -12 \cdot 12 = -144\) (not perpendicular)

After checking all combinations, none of the lines are perpendicular to each other based on the calculations.

Conclusion: The correct statement among the options provided should be that none of the lines are perpendicular. However, if required to choose among the given options, we would state that none state which lines are truly perpendicular.

Answer 2

The answers are,
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 B is perpendicular to line D . Line upper B is perpendicular to line upper D . Line A is perpendicular to line B .