Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither

Answer 1

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.

Answer 2

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.