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

User Grrrrrr
by
2.1k points

2 Answers

25 votes
25 votes
they are parallel. if the slopes are the same and the y intercept is different they are parallel
User Lupu Silviu
by
2.9k points
27 votes
27 votes

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 .

User Jens Utbult
by
2.7k points