To find the equation of a line perpendicular to the given line, we need to determine the slope of the perpendicular line. The given line has a slope of -1/3.
Since the perpendicular line has a slope that is the negative reciprocal of -1/3, we can find the perpendicular slope by taking the negative reciprocal:
Perpendicular slope = -1 / (-1/3) = 3.
Now, we can use the point-slope form of a linear equation to write the equation of the line passing through the point (-2, 5) with a slope of 3:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the coordinates of the given point and m represents the slope.
Substituting the values into the equation, we have:
y - 5 = 3(x - (-2)).
Simplifying:
y - 5 = 3(x + 2).
Expanding:
y - 5 = 3x + 6.
Finally, rearranging the equation to the slope-intercept form (y = mx + b):
y = 3x + 11.
Therefore, the equation of the line passing through the point (-2, 5) and perpendicular to the line y = (-1/3)x + 2 is y = 3x + 11.