Question

Find an equation for the line with the given properties. Perpendicular to the line x - 6y = 8; containing the point (4,4) O 1) y = 6x - 28 2) y = - (1/6) > - (14/3) 3) y = - 6x + 28 4) y = - 6x - 28

Answer 1

Option 3 -
`y=-6x+28`

Explanation:

Given : Perpendicular to the line
`x - 6y = 8`; containing the point (4,4).

To Find : An equation for the line with the given properties ?

Solution :

We know that,

When two lines are perpendicular then slope of one equation is negative reciprocal of another equation.

Slope of the equation
`x - 6y = 8`

Converting into slope form
`y=mx+c`,

Where m is the slope.

`y=(x-8)/(6)`

`y=(x)/(6)-(8)/(6)`

The slope of the equation is
`m=(1)/(6)`

The slope of the perpendicular equation is
`m_1=-(1)/(m)`

The required slope is
`m_1=-(1)/((1)/(6))`

`m_1=-6`

The required equation is
`y=-6x+c`

Substitute point (x,y)=(4,4)

`4=-6(4)+c`

`4=-24+c`

`c=28`

Substitute back in equation,

`y=-6x+28`

Therefore, The required equation for the line is
`y=-6x+28`

So, Option 3 is correct.