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=-(1)/(3)x \\ m2=-(1)/(3) \\ m1\cdot m2 \\ 3\cdot-(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\\e-1 \end{gathered}`

B is not a correct choice

`\begin{gathered} 3y=-x+7 \\ y=-(1)/(3)x+(7)/(3) \\ m2=-(1)/(3) \\ m1\cdot m2 \\ 3\cdot-(1)/(3)=-1=-1 \end{gathered}`

C is a correct choice

`\begin{gathered} x+3y=4 \\ y=-(1)/(3)x+(4)/(3) \\ m2=-(1)/(3) \\ m1\cdot m2 \\ 3\cdot-(1)/(3)=-1=-1 \end{gathered}`

D is a correct choice

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

E is not a correct choice