<u>Answer:</u>
The correct answer option is D. y = 3x - 5.
<u>Step-by-step explanation:</u>
We are given a graph of a straight line and we are to find the equation of a line which is perpendicular to this line and passes through the point.
Firstly, we will find the slope of the line using any two points on it.
![(-3, 2) (0, 1)](https://tex.z-dn.net/?f=%28-3%2C%202%29%20%280%2C%201%29)
![Slope = \frac{2-1}{-3-0} =-\frac{1}{3}](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cfrac%7B2-1%7D%7B-3-0%7D%20%3D-%5Cfrac%7B1%7D%7B3%7D)
Since the slope of a perpendicular line is a negative reciprocal of the given line so our required slope is 3.
Also, we know that the standard equation of a line is given by:
![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
So substituting the values of the given point (3, 4) and the slope to find the y-intercept:
![4=3(3)+c](https://tex.z-dn.net/?f=4%3D3%283%29%2Bc)
![c=-5](https://tex.z-dn.net/?f=c%3D-5)
Therefore, the equation of this line is y = 3x - 5.