Question

the equation of the line perpendicular to the line 2x+3y-5=0 and passing through (3,-4) is​

Answer 1

Answer:

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Answer 2

The required equation of the line perpendicular to the given line is 3x - 2y = 17

Given :

The given equation 2x + 3y - 5 = 0

To find :

The equation of the line perpendicular to the line 2x + 3y - 5 = 0 and passing through the point (3 , - 4)

Solution :

Step 1 of 3 :

Write down the given equation of the line

The given equation of the line is

2x + 3y - 5 = 0

Step 2 of 3 :

Assume the required equation of the line

Here it is given that the line is perpendicular to the line 2x + 3y - 5 = 0

Let the required equation of the line is

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

Step 3 of 3 :

Find the required equation of the line

Since the required line passes through the point (3 , - 4)

Thus from equation 1 we get

$\displaystyle \sf{ \implies (3 \times 3)} - (2 \times - 4) = k$

$\displaystyle \sf{ \implies 9 + 8 = k}$

$\displaystyle \sf{ \implies k = 17}$

Hence the required equation of the line is 3x - 2y = 17

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