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Write the equation of the line (in point-slope form) that passes through P(2, 3) and is perpendicular to the line y = 1/3 x + 2.

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Final answer:

The equation of the line in point-slope form that passes through (2, 3) and is perpendicular to y=1/3x+2 is y - 3 = -3(x - 2).

Step-by-step explanation:

To write the equation of the line in point-slope form that passes through point P(2, 3) and is perpendicular to the line y = 1/3 x + 2, we need to use the negative reciprocal of the slope of the given line. The slope of y = 1/3 x + 2 is 1/3, so the slope of the perpendicular line will be -3 (the negative reciprocal of 1/3). The point-slope form of an equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on the line.

Thus, for the point (2, 3) and the slope -3, the equation is:

y - 3 = -3(x - 2).