The equation of the line is,
.
Given that,
The equation of the line is,
![\rm y = \dfrac{1}{3} x+4\\](https://tex.z-dn.net/?f=%5Crm%20y%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20x%2B4%5C%5C)
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,
![\rm = \dfrac{1}{3}x + 4\\](https://tex.z-dn.net/?f=%5Crm%20%3D%20%5Cdfrac%7B1%7D%7B3%7Dx%20%2B%204%5C%5C)
On comparing with the standard equation of the line y = mx +c.
The slope of the line
is 1/3.
When two lines are perpendicular the relation between these slopes is,
![\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](https://tex.z-dn.net/?f=%5Crm%20m_1%5Ctimes%20m_1%20%3D%20%7B-1%7D%5C%5C%5C%5C%5Cdfrac%7B-1%7D%7B3%7D%20%5Ctimes%20m_2%20%3D%20-1%5C%5C%5C%5C-1%20%5Ctimes%20m_2%20%3D%20-1%20%5Ctimes%203%5C%5C%5C%5C-m_2%20%3D%20-3%5C%5C%5C%5Cm_2%20%3D%203)
And line contains the point (-2, -5).
Then,
![\rm y = mx +c \\\\-5 = 3 (-2) + c\\\\-5 = -6+c \\\\c = 6-5 \\\\c = 1](https://tex.z-dn.net/?f=%5Crm%20y%20%3D%20mx%20%2Bc%20%5C%5C%5C%5C-5%20%3D%203%20%28-2%29%20%2B%20c%5C%5C%5C%5C-5%20%3D%20-6%2Bc%20%5C%5C%5C%5Cc%20%3D%206-5%20%5C%5C%5C%5Cc%20%3D%201)
Therefore,
The equation of the line that is perpendicular to the given line and contains the point (-2, -5) is,
![\rm y = mx +c \\\\y = 3x +1](https://tex.z-dn.net/?f=%5Crm%20y%20%3D%20mx%20%2Bc%20%5C%5C%5C%5Cy%20%3D%203x%20%2B1)
Hence, The required equation of the line is,
.
For more details refer to the link given below.
brainly.com/question/14388443