Answer:
Perpendicular lines
Step-by-step explanation:
We are given that
[tex]y=-3x+7[/tex]
[tex]-2x+6y=3[/tex]
We have to find the pair of equations are parallel , perpendicular or neither.
Differentiate each equation w.r.t.x
[tex]m_1=\frac{dy}{dx}=-3[/tex]
Using rule :[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]
[tex]-2+6\frac{dy}{dx}=0[/tex]
[tex]6\frac{dy}{dx}=2[/tex]
[tex]m_2=\frac{dy}{dx}=\frac{2}{6}=\frac{1}{3}[/tex]
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-3}=\frac{1}{3}[/tex]
When two lines are perpendicular then ,
[tex]m_1=-\frac{1}{m_2}[/tex]
When two lines are parallel then, slope of two lines are equal.
We have
[tex]m_2=-\frac{1}{m_1}=\frac{1}{3}[/tex]
Hence, the lines are perpendicular.
