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

Solution:

The equation of a line in point slope form is

y - b = m (x - a)

Where m is the slope

(a, b) is the point

The given line is y = 3x

Point is (2, -12)

Using y = mx the slope is m = 3

It is given that the slope of a line m so the slope of a line which is perpendicular is

m = -1/m = -1/3

So we get

y - (-12) = -1/3 (x - 2)

y + 12 = -1/3 (x - 2)

Therefore, the point slope form of the line is y + 12 = -1/3 (x - 2).

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

Summary:

The point-slope form of the line passing through (2, -12) and perpendicular to y = 3x is y + 12 = -1/3 (x - 2).