Question

Line A: y = 1 2 x + 2 Line B: y = − 1 2 x + 7 Line C: y = −2x + 4 Line D: y = 1 2 x + 5 4 Which lines are perpendicular? A) A and B B) A and C C) B and C D) A and D

Answer 1

Answer:

Check the explanation.

Step-by-step explanation:

The slope-intercept form of the equation is

$y=mx + b$

• where m is the slope

• b is the y-intercept

Line A:

$y = 1 2 x + 2$

The slope of line A:

$m_A=12$     ∵ comparing with $y=mx + b$

Line B:

$y = -1 2 x + 7$

$m_B=-12$    ∵ comparing with $y=mx + b$

Line C:

$y = -2x + 4$

$m_C=-2$     ∵ comparing with $y=mx + b$

Line D:

$y = 12x + 5 4$

$m_D=12$     ∵ comparing with $y=mx + b$

As we know that the product of the slopes of perpendicular lines is -1.

i.e. their slopes are opposite of the reciprocal of each other.

Now, let us check the OPTIONS:

Option A)  A and B

Check:

$m_A=12$  

$m_B=-12$

As the product of the slopes A and B is NOT -1, so the lines A and B are not perpendicular. Hence, option A is NOT true.

Option B)  A and C

$m_A=12$  

$m_C=-2$

As the product of the slopes A and C is NOT -1, so the lines A and C are not perpendicular. Hence, option B is NOT true.

Option C)  B and C

$m_B=-12$

$m_C=-2$

As the product of the slopes B and C is NOT -1, so the lines B and C are not perpendicular. Hence, option C is NOT true.

Option D)  A and D

$m_A=12$  

$m_D=12$

As the product of the slopes A and D is NOT -1, so the lines A and D are not perpendicular. Hence, option D is NOT true.

Therefore, NO OPTION is correct.