Question

Which lines are perpendicular to 3x – y = 10? Select all that apply.

Answer 1

Answer:

the answer should be C

Step-by-step explanation:

the gradient of C is -1/3 that perpendicular to the question

Answer 2

Answer:

Option C - x + 3y = 27

Step-by-step explanation:

To find : Which lines are perpendicular to  $3x-y = 10$ ? Select all that apply.

Solution :

We know that,

When two lines are perpendicular then the product of their slope is -1.

The slope is given by $y=mx+c$ where, m is the slope.

So, the slope of the given equation  $3x-y = 10$  is

$y=3x-10$

Slope is $m_1=3$.

Now find slope of others lines,

A) $y=3x+5$

Slope is $m_2=3$

Product of the slope is $m_1\times m_2=-1$

$3\times 3=-1$

$9\neq -1$

No, this line is not perpendicular to given line.

B) $y=-13x+17$

Slope is $m_2=-13$

Product of the slope is $m_1\times m_2=-1$

$3\times -13=-1$

$-39\neq -1$

No, this line is not perpendicular to given line.

C) $x+3y=27$

$y=-\frac{1}{3}x+9$

Slope is $m_2=-\frac{1}{3}$

Product of the slope is $m_1\times m_2=-1$

$3\times -\frac{1}{3}=-1$

$-1= -1$

Yes, this line is perpendicular to given line.

D) $y-2=13(3x+36)$

$y=39x+468+2$

$y=39x+470$

Slope is $m_2=39$

Product of the slope is $m_1\times m_2=-1$

$3\times 39=-1$

$117\neq -1$

No, this line is not perpendicular to given line.

Therefore, option C is correct.