Use the table to answer the question. Item 5 5 of 24 Line Equation Item 6 Line A y=2x-3 Item 7 Line By=2x+5 Item 8 Line Cy = 1 -2 Item 9 1 Line D y=x+2 Item 10 Given the linear equations in the table, which of the following statements is true? Item 11 Line B is perpendicular to line D. Item 12 (1 point) < Line A is perpendicular to line C. Line C is perpendicular to line D. Line A is perpendicular to line B.

Answer 1

To determine which statements about the lines defined by the equations in the table are true regarding perpendicularity, we need to analyze their slopes.

1. Line A: y = 2x - 3

   • Slope (m) = 2

2. Line B: y = 2x + 5

   • Slope (m) = 2

3. Line C: y = -2

   • This is a horizontal line, which means its slope (m) = 0.

4. Line D: y = x + 2

   • Slope (m) = 1

Perpendicular Line Rule: Two lines are perpendicular if the product of their slopes is -1, which means if one has a slope of m, the other must have a slope of -1/m.

Now, let's evaluate the given statements:

• Statement: Line B is perpendicular to line D.

  • Slope of Line B = 2 and Slope of Line D = 1.
  • \(2 \times 1 \neq -1\). Not perpendicular.

• Statement: Line A is perpendicular to line C.

  • Slope of Line A = 2 and slope of Line C = 0.
  • \(2 \times 0 \neq -1\). Not perpendicular.

• Statement: Line C is perpendicular to line D.

  • Slope of Line C = 0 and slope of Line D = 1.
  • \(0 \times 1 \neq -1\). Not perpendicular.

• Statement: Line A is perpendicular to line B.

  • Slope of Line A = 2 and slope of Line B = 2.
  • \(2 \times 2 \neq -1\). Not perpendicular.

None of the statements provided are true regarding the perpendicularity of the lines. Therefore, based on the data given, it appears that none of the listed options are correct.