Respuesta :
Answer:
the answer should be C
Step-by-step explanation:
the gradient of C is -1/3 that perpendicular to the question
Answer:
Option C - x + 3y = 27
Step-by-step explanation:
To find : Which lines are perpendicular to [tex]3x-y = 10[/tex] ? 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 [tex]y=mx+c[/tex] where, m is the slope.
So, the slope of the given equation [tex]3x-y = 10[/tex] is
[tex]y=3x-10[/tex]
Slope is [tex]m_1=3[/tex].
Now find slope of others lines,
A) [tex]y=3x+5[/tex]
Slope is [tex]m_2=3[/tex]
Product of the slope is [tex]m_1\times m_2=-1[/tex]
[tex]3\times 3=-1[/tex]
[tex]9\neq -1[/tex]
No, this line is not perpendicular to given line.
B) [tex]y=-13x+17[/tex]
Slope is [tex]m_2=-13[/tex]
Product of the slope is [tex]m_1\times m_2=-1[/tex]
[tex]3\times -13=-1[/tex]
[tex]-39\neq -1[/tex]
No, this line is not perpendicular to given line.
C) [tex]x+3y=27[/tex]
[tex]y=-\frac{1}{3}x+9[/tex]
Slope is [tex]m_2=-\frac{1}{3}[/tex]
Product of the slope is [tex]m_1\times m_2=-1[/tex]
[tex]3\times -\frac{1}{3}=-1[/tex]
[tex]-1= -1[/tex]
Yes, this line is perpendicular to given line.
D) [tex]y-2=13(3x+36)[/tex]
[tex]y=39x+468+2[/tex]
[tex]y=39x+470[/tex]
Slope is [tex]m_2=39[/tex]
Product of the slope is [tex]m_1\times m_2=-1[/tex]
[tex]3\times 39=-1[/tex]
[tex]117\neq -1[/tex]
No, this line is not perpendicular to given line.
Therefore, option C is correct.
