Question

Thank you so much!!!

Answer 1

`\fbox{\begin{minipage}{16em}Option D: y = (4/7)x + 8 is correct\end{minipage}}`

Explanation:

(1) A typical form of equation of a line is:

`y = Mx + b`

with,
`M` is slope and
`b` is y-intercept.

(2) Another straight line has equation in form of:

`y = Nx + c`

with
`N` is slope and
`c` is y-intercept

(3) If these two lines are perpendicular, according to the property of two perpendicular lines on the two-dimensional plane, we have:

`M` x
`N` = -1

(4) Transform the given equation of original line into typical form:

`7x + 4y = -24\\`

<=>
`4y = -7x - 24`

<=>
`y = ((-7)/(4))x - (24)/(4)`

<=>
`y = ((-7)/(4))x - 6`

=>
`M = (-7)/(4)`

=>
`N = (-1)/(M) = (-1)/((-7)/(4) ) = (-4)/(-7) = (4)/(7)`

=> Option D:
`y = ((4)/(7))x + 8` is correct (Slope =
`(4)/(7)`)

Hope this helps!

:)