Question #32820

1 Answer
Jan 21, 2016

Given

l_1: y=m_1x+q_1
l_2: y=m_2x+q_2

l_1 // l_2

when:

m_1=m_2

Explanation:

An equation could be given in the follow forms:

  1. y=mx+q

m is the slope; q is the y axis intercept
2. ay+bx+c=0

This form could be write like the first one;
y=-b/ax-c/a
=> m=-b/a; q=-c/a

given:

l_1: y=m_1x+q_1
l_2: y=m_2x+q_2

l_1 // l_2

when:

m_1=m_2

if q_1=q_2, then l_1 is coincident with l_2

You have l_1:y=6=>y=0*x+6=>m=0

therefore the parallel lines to the given one are in the form:

y=k => all the horizontal lines