This is the Important question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD.

Here you have to find the equation of a straight line perpendicular to a line and having same y-intercept as given in the question.

This is the Question Number 13, Exercise 12.2 of M.L Aggarwal.

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# Find the equation of a straight line perpendicular to the line 3x – 4y + 12 = 0 and having same y-intercept as 2x – y + 5 = 0.

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Given line: 3x – 4y + 12 = 0

The slope of the line is given by

3x – 4y + 12 = 0 ⇒ 4y = 3x + 12

y = (3/4) x + 3

Thus, slope (m

_{1}) = ¾Now, let the slope of the line perpendicular to the given line be taken as m

_{2}So,

m

_{1}x m_{2}= -1(3/4) x m

_{2}= -1m

_{2}= -4/3And given, the y-intercept of the line is same as 2x – y + 5 = 0

⇒ y = 2x + 5

So, the y-intercept is 5 = c.

Hence, the equation of line is given by

y = m

_{2}x + cy = (-4/3) x + 5

3y = -4x + 15

4x + 3y = 15