Respuesta :
The equation of the line is, [tex]\rm y = 3x + 1[/tex].
Given that,
The equation of the line is,
[tex]\rm y = \dfrac{1}{3} x+4\\[/tex]
And contains the point (-2, -5).
We have to determine,
What is the equation of the line that is perpendicular to the given line?
According to the question,
The equation of the line is,
[tex]\rm = \dfrac{1}{3}x + 4\\[/tex]
On comparing with the standard equation of the line y = mx +c.
The slope of the line [tex]m_1[/tex] is 1/3.
When two lines are perpendicular the relation between these slopes is,
[tex]\rm m_1\times m_1 = {-1}\\\\\dfrac{-1}{3} \times m_2 = -1\\\\-1 \times m_2 = -1 \times 3\\\\-m_2 = -3\\\\m_2 = 3[/tex]
And line contains the point (-2, -5).
Then,
[tex]\rm y = mx +c \\\\-5 = 3 (-2) + c\\\\-5 = -6+c \\\\c = 6-5 \\\\c = 1[/tex]
Therefore,
The equation of the line that is perpendicular to the given line and contains the point (-2, -5) is,
[tex]\rm y = mx +c \\\\y = 3x +1[/tex]
Hence, The required equation of the line is, [tex]\rm y = 3x + 1[/tex].
For more details refer to the link given below.
https://brainly.com/question/14388443
