USE SLOPE TO SAY THE LINES ARE PARALLEL PERPENDICULAR OR NEITHER

Parallel lines :

Parallel lines will have the same slope.

f m₁ and m₂ are slopes of the 1^st and 2^nd line, then

m₁ = m₂

Perpendicular Lines :

Lines that intersect at right angles are called perpendicular lines.

If the product of the slopes of two nonvertical lines is -1, then the lines are perpendicular

m₁ x m₂ = -1

Determine whether the pairs of slopes listed are parallel, perpendicular or neither.

Problem 1 :

m₁ = 2, m₂ = -1/2

Solution :

Finding the product of slopes,

m_{1 x} m₂ = 2 (-1/2) = -1

Since the product of slopes is equal to -1, the lines are perpendicular.

Problem 2 :

m = 3, m = -3

Solution :

By considering the slopes.

So, they are neither.

Problem 3 :

m = -4, m =-1/4

Solution :

The slopes are not equal, so they are not parallel.

The product of their slopes is not equal to -1, so they are not perpendicular.

So, they are neither.

Problem 4:

m = 10, m = -.1

Solution :

There is no relationship between slopes. So they are neither.

Problem 5 :

m = 2, m = 3

Solution :

There is no relationship between slopes. So they are neither.

Problem 6 :

m = 4/5, m = 8/10

Solution :

m = 4/5, m = 8/10

Simplifying 8/10, we will get 4/5.

Determine whether the pair of lines listed is parallel, perpendicular or neither. Show your work.

Problem 7 :

y = (1/4)x - 3

y= - 4x + 3

Solution :

Slope of the line y = (1/4)x - 3 :

m₁ = 1/4

Slope of the line y = -4x + 3 :

m₂ = -4

m₁ m₂ = (1/4) (-4) ==> -1

So, the lines are perpendicular.

Problem 8 :

y = 2x - 4

y = -2x + 5

Solution :

Slope of the line y = 2x - 4:

m₁ = 2

Slope of the line y = -2x + 5 :

m₂ = -2

The slopes are not equal, their product is not equal to -1. So, they are neither.

Problem 9 :

3x + y = 5

y = (-1/3)x + 2

Solution :

Slope of the line 3x + y = 5 :

y = -3x + 5

m₁ = -3

Slope of the line y = (-1/3)x + 2 :

m₂ = -1/3

The slopes are not equal, their product is not equal to 1. So, they are neither.