Question

Select all the equations that represent lines perpendicular to Y= 3x+4.A. Y= -1/3xB. 6x-2y=4C. 3y= -x+7D. X+3y=4E. y=3x-10

Answer 1

if two lines are perpendicular it is true that:

$m1\cdot m2=-1$

For the line:

$\begin{gathered} y=3x+4 \\ m1=3 \end{gathered}$

Let's check every line:

$\begin{gathered} y=-\frac{1}{3}x \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}$

So, A is a correct choice

$\begin{gathered} 6x-2y=4 \\ y=3x-2 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}$

B is not a correct choice

$\begin{gathered} 3y=-x+7 \\ y=-\frac{1}{3}x+\frac{7}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}$

C is a correct choice

$\begin{gathered} x+3y=4 \\ y=-\frac{1}{3}x+\frac{4}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}$

D is a correct choice

$\begin{gathered} y=3x-10 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}$

E is not a correct choice