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Find the equation of straight line passing through (2, 3) an...

Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x+2y+4=0

A.

3y = 5x - 2

B.

y = 53×2

C.

None of these

D.

3y = 2x + 5

Correct answer is D

3x+2y+4=0

Rearrange:

2y=3x4

Divide both sides by 2

y = 3×42

y = 32×2

∴ the gradient of the line 3x + 2y + 4 = 0 is 32

If two lines are perpendicular to each other ∴ m1xm2 = -1

Let m1=32

From the equation of a line which is given as m = \frac {y - y_1}{x - x_1} where (x_1, y_1) = (2,3)

\therefore \frac {2}{3} = \frac {y - 3}{x - 2}

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

=3y - 9 = 2 x -4

=3y = 2 x -4 + 9

∴ 3y = 2x + 5