Question

13. Which equation represents the line that passes through the point (4,-5) and is

perpendicular to y = 1/2x + 8?

Answer 1

y = - 2x + 3

Explanation:

since the line passing through ( 4, - 5 ) is perpendicular to y = 1/2 x + 8, product of the slope of the lines will be - 1.

That is ,

`m_1 * m_ 2 = - 1`
`[ \ where \ m_ 1 = (1)/(2) \ ]`

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

Find the equation the line perpendicular to the given line :

`( y - y_2 ) = m_ 2 ( x - x_ 2 ) \ , [ \ where \ (x_2 , y_2 ) = ( 4 , -5 ) \ ]`

`( y - ( -5)) = -2 ( x - 4)\\\\( y + 5 ) = - 2 x + 8\\\\y = -2x + 8 - 5 \\\\y = -2x + 3`