<u>Given</u>:
Given that the graph of the equation of the line.
The line that is perpendicular to the given line and passes through the point (2,-1)
We need to determine the equation of the line perpendicular to the given line.
<u>Slope of the given line:</u>
The slope of the given line can be determined by substituting any two coordinates from the line in the slope formula,
Substituting the coordinates (-1,3) and (2,2), we get;
Thus, the slope of the given line is
<u>Slope of the perpendicular line:</u>
The slope of the perpendicular line can be determined by
Substituting , we get;
simplifying, we get;
Thus, the slope of the perpendicular line is 3.
<u>Equation of the perpendicular line:</u>
The equation of the perpendicular line can be determined using the formula,
Substituting and the point (2,-1) in the above formula, we have;
Thus, the equation of the perpendicular line is
Hence, Option d is the correct answer.
