Parallel Lines
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For example, without drawing the graphs of y = −5x + 9 and y = −5x − 23, we can claim that their graphs are parallel, since both have the slope −5.
Example 1
Write the equation of the line parallel to y = 3x −1 that passes through the point (4, −1) in point−slope form.
Since the new line is parallel to our given line, it will have the same slope.
m = 3
Now, continue as you learned in the last section.
y + 1 = 3(x − 4)
Example 2
Determine if these lines are parallel.
Line 1: 2x − 2y = 10
Line 2: 7y = −7x − 21
First, we have to change line 1 and 2 into the slope intercept form.
Line 1:
2x − 2y = 10
−2y = −2x + 10
y = x − 5 (so the slope is +1)Line 2:
7y = −7x − 21
y = −x − 3 (so the slope is −1)
Since the slopes are not the same, one is +1 and the other is −1, the lines are not parallel.
