Determine if the pair of lines are parallel perpendicular or intersecting

Answer:

1. y= 2/3x + 4, and y = 2/3x - 1 are parallel

2. y = 1/3x - 3  and y = 2x + 5 are perpendicular

3. y =2/5x +4 and y = 0.2x - 1 are intersecting

4. y = -x + 13 and y = x-14 are perpendicular

Step-by-step explanation:

The equation of lines are solved and parallel lines are

a) y = 2/3x + 4 , y = ( 2/3 )x - 1

Perpendicular lines , y = -( 1/2 )x - 3 , y = 2x + 5

Intersecting lines

a) y = ( 2/5 )x + 4 , y = 0.2x - 1

b) y = -x + 13 , y = x - 14

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

y = 2/3x + 4 , y = ( 2/3 )x - 1

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = 2/3

So , the slopes of the two lines are same and they are parallel lines

And , y = -( 1/2 )x - 3 , y = 2x + 5

The slopes are negative reciprocals of each other , so they are perpendicular lines

Now , the intersecting lines are a) y = ( 2/5 )x + 4 , y = 0.2x - 1

b) y = -x + 13 , y = x - 14

Hence , the equation of line is solved

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