Question

Are the two lines parallel, perpendicular,
or neither?
y = 3x -4 and 3x +9y = 18

Answer 1

they are parallel. if the slopes are the same and the y intercept is different they are parallel

Answer 2

Prerequisites :-

1) The product of slope of two perpendicular lines is-1 .

2) The slope of two parallel lines is same .

Given two lines to us are ,

• 
  `y = 3x - 4`

This line is in slope intercept form which is
`y = mx + c` . Comparing to which we get ,

• 
  `m_1 = 3`

Again , the second line given to us is ,

• 
  `3x + 9y = 18`

Convert it into slope intercept form , we have ,

`\implies 3( x + 3y ) = 18`

Divide both sides by 3 ,

`\implies x + 3y = 6`

Solve for y ,

`\implies y = (-x)/(3) + 2`

On comparing to the slope intercept form ,

• 
  `m_2 = (-1)/(3)`

And the product both the slopes is ,

`\implies m_1 * m_2 = (-1)/(3)* 3 =\boxed{\red{-1}}`

Hence the given two lines are perpendicular .