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Which line passes through (1, 2) and is perpendicular to $2 x + 3 y = 6$ ?

Competition practiceGeometry

A $3 x - 2 y + 1 = 0$
B $2 x + 3 y - 8 = 0$
C $3 x + 2 y - 7 = 0$
D $2 x - 3 y + 4 = 0$

Step-by-Step Solution

The given line has slope

- \frac{2}{3}

, so a perpendicular has slope

\frac{3}{2}

. Through (1, 2):

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

, i.e.

3 x - 2 y + 1 = 0

.

Answer: A)

3 x - 2 y + 1 = 0

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