Question

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?

Answer 1

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 .

Line A
is perpendicular to line C
.
Line upper A is perpendicular to line upper C .

Line C
is perpendicular to line D
.

Answer 2

To determine which of the following statements is true, we must analyze the given equations.

Line A: y = 2x - 3
Line B: y = 2x + 5
Line C: y = -12x - 2
Line D: y = 12x + 2

To identify the true statement, we need more information.

Answer 3

Based on the given equations, we can determine if the lines are perpendicular by looking at the slopes.

The slope of a line in the form y = mx + b is equal to the coefficient of x, which is m.

For Line B, the slope is 2.
For Line D, the slope is 12.

If two lines are perpendicular, their slopes are negative reciprocals of each other. This means that when you multiply the slopes together, the result is -1.

For Line B and Line D:
(2) * (12) = 24, which is not equal to -1. Therefore, Line B is not perpendicular to Line D.

For Line A and Line B:
The slope of Line A is 2.
The slope of Line B is also 2.

(2) * (2) = 4, which is not equal to -1. Therefore, Line A is also not perpendicular to Line B.

For Line A and Line C:
The slope of Line A is 2.
The slope of Line C is -12.

(2) * (-12) = -24, which is equal to -1. Therefore, Line A is perpendicular to Line C.

For Line C and Line D:
The slope of Line C is -12.
The slope of Line D is 12.

(-12) * (12) = -144, which is equal to -1. Therefore, Line C is perpendicular to Line D.

In summary, the true statement is:

Line C is perpendicular to Line D.