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Example 1: Pair of lines are parallel.
Example 2: Pair of lines are perpendicular.
Example 3: Pair of lines are not parallel nor perpendicular.
Example 4: Pair of lines are perpendicular.
Example 5: Pair of lines are parallel.
Example 6: Pair of lines are parallel.
Example 7: Pair of lines are perpendicular.
Example 8: Pair of lines are not parallel nor perpendicular.
What is the slope of the line in the slope-intercept form of the line?
If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.
For example 1:
y = 3x + 4 and y = 3x +7
The slopes of both lines are equal hence, these pair of lines are parallel.
For example 2:
y = -4x + 1 and 4y = x + 3
Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.
For example 3:
y = 2x - 5 and y = 5x -5
In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.
For example 4:
y = -1/3x + 2 and y = 3x - 5
Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.
For example 5:
y = 3/5x - 3 and 5y = 3x - 10
The slopes of both lines are equal hence, these pair of lines are parallel.
For example 6:
y = 4 and 4y = 6
The slopes of both lines are equal hence, these pair of lines are parallel.
For example 7:
y = 7x + 2 and x + 7y = 8
Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.
For example 8:
y = 5/6x - 6 and x + 5y = 4
In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.
Hence,
Example 1: Pair of lines are parallel.
Example 2: Pair of lines are perpendicular.
Example 3: Pair of lines are not parallel nor perpendicular.
Example 4: Pair of lines are perpendicular.
Example 5: Pair of lines are parallel.
Example 6: Pair of lines are parallel.
Example 7: Pair of lines are perpendicular.
Example 8: Pair of lines are not parallel nor perpendicular.
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