What is the equation, in slope-intercept form, of the line
that is perpendicular to the given line and passes through
the point (2, -1)?
y=- 2x - 2 / 2
y=- 2x - 5 / 5
y = 3x - 3
y = 3x - 7

Given:

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.

Slope of the given line:

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

Slope of the perpendicular line:

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.

Equation of the perpendicular line:

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.