Final answer:
The equation of the line is y = -1/3x + 5/3.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other. The given line has a slope of 3, so the perpendicular line will have a slope of -1/3. Using the point-slope form of a line, we have:
y - y1 = m(x - x1)
Plugging in the values (2, -3) for (x1, y1) and -1/3 for m, we get:
y - (-3) = -1/3(x - 2)
Further simplifying, we have the equation in slope-intercept form:
y = -1/3x + 5/3
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