Find the equation of a line drawn perpendicular to the line through the point, where it meets the y-axis.

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Solution

The equation of the given line is.

This equation can also be written as 3x + 2y – 12 = 0

, which is of the form y = mx + c

∴Slope of the given line

∴Slope of line perpendicular to the given line

Let the given line intersect the y-axis at (0, y).

On substituting x with 0 in the equation of the given line, we obtain

∴The given line intersects the y-axis at (0, 6).

The equation of the line that has a slope of and passes through point (0, 6) is

Thus, the required equation of the line is.

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