Question

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

A. y = 3x + 5
B. y = –13x + 17
C. x + 3y = 27
D. y – 2 = 13(3x + 36)

Answer 1

the answer should be C

Explanation:

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

Answer 2

Option C - x + 3y = 27

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* m_2=-1`

`3* 3=-1`

`9\\eq -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* m_2=-1`

`3* -13=-1`

`-39\\eq -1`

No, this line is not perpendicular to given line.

C)
`x+3y=27`

`y=-(1)/(3)x+9`

Slope is
`m_2=-(1)/(3)`

Product of the slope is
`m_1* m_2=-1`

`3* -(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* m_2=-1`

`3* 39=-1`

`117\\eq -1`

No, this line is not perpendicular to given line.

Therefore, option C is correct.