Question

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

Answer 1

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 ,

$\implies y = \dfrac{-x}{3} + 2$

On comparing to the slope intercept form ,

• $m_2 = \dfrac{-1}{3}$

And the product both the slopes is ,

$\implies m_1 \times m_2 = \dfrac{-1}{3}\times 3 =\boxed{\red{-1}}$

Hence the given two lines are perpendicular .

Answer 2

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