Mathematics: Tell whether the lines for each pair of equations are parallel, perpendicular, or neither y= -3x + 7 -2x+6y=3

Answer; ok?Step-by-step explanation:...

Tell whether the lines for each pair of equations

toyensianelys130

03.01.2022

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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