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in Straight Lines by (15 points)
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The equation of a straight line that passes through the point (3,4) and perpendicular to line 3x + 2y + 5 = 0.

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2 Answers

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by (14.8k points)

Perpendicular lines have slopes that are negative reciprocals of one another.  This equation is:

y = -(3/2)x - 5/2    with slope -3/2

So the slope of the perpendicular line will be 2/3

To find the y intercept we substitute: 4 = (2/3)3 + c    or c = 2

So the equation of a perpendicular line passing through point (3,4) is:

y = (2/3)x + 2

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by (46.5k points)

The equation of a line perpendicular to 3x + 2y + 5 = 0 is 2x - 3y + λ = 0 .........(i)

This passes through the point (3, 4)

∴ 3 × 2 − 3 × 4 + λ = 0

⇒ λ = 6

Putting λ = 6 in (i) we get 2x − 3y + 6 = 0 which is the required equation.

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