Iwill give ! (6 points! )

what is the equation of the line that passes through the point (-2,3) and that is perpendicular to the line represented by 3x - 2y = -2?

2x + 3y = 5

2x + 3y + 7

-2x + 3y + 5

3x = 2y + -12

asap!

OPTION A: 2x + 3y = 5

Step-by-step explanation:

The product of slopes of two perpendicular lines is -1.

We rewrite the given equation as follows:

2y = 3x + 2

⇒ y =

The general equation of the line is: y = mx + c, where 'm' is the slope of the line.

Here, m = .

Therefore, the slope of the line perpendicular to the line given = because .

To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:

                                  y - y₁ = m(x - x₁)

The point is: (x₁, y₁) = (-2, 3)

Therefore, the equation is:

y - 3 = (x + 2) $

⇒ 3y - 9 = -2(x + 2)

⇒ 3y - 9 = -2x - 4

⇒ 2x + 3y = 5 is the required equation.