Question

Which equation is perpendicular

Answer 1

option A

Explanation:

`y - 9 = (2)/(3) (x + 7)\\\\ y - 9= (2)/(3) x + (14)/(3)\\\\ y = (2)/(3) x + (14)/(3) + 9\\\\y = (2)/(3)x + (14 +27)/(3)\\\\y = (2)/(3)x + (41)/(3)\\\\`

Therefore, slope of the given line is

`m_ 1 = \ (2)/(3)`

Find the slope of the new line

The product of slope of lines perpendicular to each other = - 1

That is ,

`m_ 1 * m_2 = - 1\\\\(2)/(3) * m_ 2 = - 1\\\\m_ 2 = - (3)/(2)`

Find the equation of the line.

`Let \the \ given \ points \ be \ ( x_ 2 , y _ 2 ) = ( 2 , 3 ) \\\\(y- y_2) = m_2 (x - x_ 2)\\\\( y - 3 ) = - (3)/(2)(x - 2)\\\\y = -(3)/(2)x + (3 * 2)/(2) + 3\\\\y = - (3)/(2) x +3+3\\\\y = - (3)/(2) x +6\\\\`