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 .

Question

Select One

Answer 1

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.