Question

Thank you so much!!!

Answer 1

Answer:

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

Step-by-step 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:

      $7x + 4y = -24$

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

<=>  $y = (\frac{-7}{4})x - \frac{24}{4}$

<=> $y = (\frac{-7}{4})x - 6$

=> $M = \frac{-7}{4}$

=> $N = \frac{-1}{M} = \frac{-1}{\frac{-7}{4} } = \frac{-4}{-7} = \frac{4}{7}$

=> Option D: $y = (\frac{4}{7})x + 8$ is correct (Slope = $\frac{4}{7}$)

Hope this helps!

:)