Question

Y=3x+4 , 9x-3y=-6 do the lines intersect or are they parallel or are they perpendicular

Answer 1

Lines are parallel.

Explanation:

The given lines are
`y=3x+4,\ 9x-3y=6`

Rearrange the equation in the slope intercept form that is
`y=mx+b` where
`m` is the slope.

First Line:

`y=3x+4`

compare it with
`y=mx+b`

slope (
`m_(1)`) of first line
`=3`

Second Line:

`9x-3y=6\\9x-6=3y\\3y=9x-6`

divide both by
`3`

`y=3x-3`

compare it with
`y=mx+b`

slope
`(m_(2))` of second line
`=3`

Since slope of two lines are equal

`m_(1)=m_(2)=3`

hence these lines are parallel.