Question

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

Answer 1

Answer:

Equation of the line = 3x + 2y + 5 = 0

Step-by-step explanation:

Given:

• The line 2x - 3y + 4 = 0
• Point (-3, 2)

To Find:

Equation of a line perpendicular to the given line and passing through the given point

Solution:

First finding the slope of the given line, 2x - 3y + 4 = 0

2x - 3y = -4

-3y = -4 - 2x

y = 4/3 + 2x/3

Hence slope of the line is 2/3.

Now given that the required line is perpendicular to this line.

Hence slope of the required line = -3/2

Now the equation of the line passing through a given point and slope is given by,

$\sf y-y_0=m(x-x_0)$

where m is the slope of the line.

Substitute the data,

$\sf y-2=-\dfrac{3}{2}(x+3)$

2y - 4 = -3x - 9

3x + 2y + 5 = 0

Hence the equation of the required line is 3x + 2y + 5 = 0