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OmThePro

Answer: [tex]y = \frac{-3}{2} x + 9[/tex]

I have reduced my explanation as per your request.

First, take the equation [tex]2x - 3y = 12[/tex], and convert it into slope intercept form. You get [tex]y = \frac{2}{3} x + 4[/tex]. Since the line is perpendicular, then you take the negative reciprocal of [tex]\frac{2}{3}[/tex]. That is [tex]\frac{-3}{2}[/tex]. Then, write the equation of the new line as [tex]y - 6 = \frac{-3}{2} (x - 2)[/tex]. Convert the point slope equation into slope intercept and you get [tex]y = \frac{-3}{2} x + 9[/tex].

Answer:

y = -3/2x - 3.

Step-by-step explanation:

2x - 3y = 12

Find the slope of this line

-3y = - 2x + 12

y = 2/3 x - 4   so its slope id 2/3.

The slope of a line perpendicular to it has slope  - 1 / 2/3

= -3/2.

Using y - y1 = m(x - x1) we have

y - 6 = -3/2(x - 2)

y = -3/2 x + 3 + 6

y = -3/2x + 9 is the answer.

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