Question

Question #32820

Answer 1

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