Verified Answer :

beyourself0018

6y = -x - 7 
y= 6x - 3 
__________________ 

y = x/6 + 7/6 
y= 6x - 3 

Compare the gradients, one is 1/6, one is 6. These are not parallel because they aren't the same, and not perpendicular because they aren't negative reciprocals. Therefore, neither.

lublana

Answer:

Perpendicular lines

Step-by-step explanation:

We are given that

\(y=-3x+7\)

\(-2x+6y=3\)

We have to find the pair of equations are parallel , perpendicular or neither.

Differentiate each equation w.r.t.x

\(m_1=\frac{dy}{dx}=-3\)

Using rule :\(\frac{dx^n}{dx}=nx^{n-1}\)

\(-2+6\frac{dy}{dx}=0\)

\(6\frac{dy}{dx}=2\)

\(m_2=\frac{dy}{dx}=\frac{2}{6}=\frac{1}{3}\)

\(m_2=-\frac{1}{m_1}=-\frac{1}{-3}=\frac{1}{3}\)

When two lines are perpendicular then ,

\(m_1=-\frac{1}{m_2}\)

When two lines are parallel then, slope of two lines are equal.

We have

\(m_2=-\frac{1}{m_1}=\frac{1}{3}\)

Hence, the lines are perpendicular.

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