The relationship between the lines are
1) Parallel
2) Neither parallel nor perpendicular
3) perpendicular
4) perpendicular
5) Parallel
6) perpendicular
Relationship between slopes of parallel and perpendicular lines.
Lines are parallel if their slopes are equal. Lines are perpendicular if the product of their slopes is -1.
In standard form equation of a line is represented as
y = mx + b
where
m is slope
b is y-intercept
Given
1) y = 3x -7 and y = 3x + 1
Their slope is 3
The slopes are equal, therefore they are parallel.
Given:
y = -2x/5 + 3 and y = 2x/5 + 8
m₁ = -2/5, m₂ = 2/5
Product of slope = -2/5 * 2/5
= -4/25
For two lines to be perpendicular the product of their slopes gives -1.
They are neither parallel nor perpendicular.
Given:
y = -x/4 and y = 4x -5
m₁ = -1/4, m₂ = 4
product of slopes = -1/4 * 4 = -1
They are perpendicular
Given
x - 2y = 18
2x + y = 6
Express both in standard form
-2y = -x + 18
y = x/2 -9
y = -2x +6
m₁ = 1/2, m₂ = 2
Product of slopes = 1/2* -2 = -1
They are perpendicular
Given:
x = 4 and x = -6
x - 4 = 0 and x + 6 = 0
m₁ =m₂ =1
Their slope is 1
They are parallel
Given:
x = 1 and y = -8
x - 1 = 0 and y + 8 = 0
No slope
They are perpendicular