Question

find the equation of a straight line that passes through the point (3,4) and perpendicular to the line 3 X + 2 Y + 5 =0

class 11
straight line

Answer 1

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Answer 2

Answer:

3y -2x + 6 = 0

Step-by-step explanation:

General equation of a linear line : y = mx + c

Gradient of the Perpendicular lines is its reciprocal

Find the gradient:

3x + 2y + 5 = 0

2y = -3x - 5

y = -3/2 x - 5/2

⇒ The gradient is -3/2

⇒ The gradient of the perpendicular line is 2/3

Find the y-intercept:

y = mx + c

At point (3, 4) and gradient = 2/3

4 = 2/3 (3) + c

4 = 2 + c

c = 2

Find the equation:

y = mx + c

y = 2/3 x + 2

3y = 2x + 6

3y -2x + 6 = 0

Answer: 3y -2x + 6 = 0