What is the point-slope form of the line passing through (2, 12) and perpendicular to y = 3x?

To find the point-slope form of a line, we need two key pieces of information: a point through which the line passes and the slope of the line.

First, we are given a point, which is (2, 12). Next, we need to determine the slope of the line perpendicular to the line described by the equation y = 3x.

The slope of the line y = 3x is 3. When finding a line that is perpendicular to another, we use the negative reciprocal of the original slope. Thus, the slope of our new line will be:

m = -1/3

Now we have a point (2, 12) and the slope (-1/3). The point-slope form of a line is given by the formula:

y – y₁ = m(x – x₁)

Substituting the point and slope into the formula:

y – 12 = -1/3(x – 2)

This is the point-slope form of the line we were looking for!