Given:
Equation of line is
.
A line is perpendicular to the given line and passes through (-3,7).
To find:
The point slope form of the perpendicular line.
Solution:
Point slope form of a line is
...(i)
where,
is the point from which the line is passing through and m is slope.
We have,
...(ii)
From (i) and (ii), we get
![m_1=2](https://tex.z-dn.net/?f=m_1%3D2)
Product of slopes of two perpendicular lines is -1.
![m_1\times m_2=-1](https://tex.z-dn.net/?f=m_1%5Ctimes%20m_2%3D-1)
![2\times m_2=-1](https://tex.z-dn.net/?f=2%5Ctimes%20m_2%3D-1)
![m_2=-\dfrac{1}{2}](https://tex.z-dn.net/?f=m_2%3D-%5Cdfrac%7B1%7D%7B2%7D)
So, slope of perpendicular line is
.
Point slope form of the perpendicular line is
![y-(7)=-\dfrac{1}{2}(x-(-3))](https://tex.z-dn.net/?f=y-%287%29%3D-%5Cdfrac%7B1%7D%7B2%7D%28x-%28-3%29%29)
![y-7=-\dfrac{1}{2}(x+3)](https://tex.z-dn.net/?f=y-7%3D-%5Cdfrac%7B1%7D%7B2%7D%28x%2B3%29)
Therefore, the correct option is C.