Any two lines are parallel if and only if their slopes are equal.
Example:
y = 2x + 3 and 2y = 4x + 7, check the given two lines are parallel.
Solution:
Given that,
y = 2x + 3 I
2y = 4x + 7 II
First we find the slopes of the given lines, if the slopes of the lines are equal then the two lines are parallel.
Slope of the first line,
y = 2x + 3
This is in the form of y = mx + c
Slope for this line is m
m = 2
Therefore, the slope of the first line is 2.
Slope for the second line,
i.e., 2y = 4x + 7
Convert this line in the form of y = mx + c
y = (4/2)x + 7/2.
y = 2x + 7/2
Slope m = 2
The slope of the second line is 2
Therefore, the slopes of two lines are equal so the given lines are parallel.
Directions: Check if the given lines are parallel. Also draw at least 5 parallel lines and show that their slopes are equal.
