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Writing Equations of Perpendicular Lines

Writing Equations of Perpendicular Lines 1.7 - Solution

arrow_back Return to Writing Equations of Perpendicular Lines
a
Two lines are parallel if their slopes are identical and their -intercepts are not equal. Note that almost all equations are already written in slope-intercept form. Let's write III and IV in that form as well.

It is now easier to identify the slopes.

Line Equation Slope
(I)
(II)
(III)
(IV)
(V)

We can see that two slopes appear more than once. Now, to be sure that they are parallel, they must not have the same -intercept.

Lines -intercepts Parallel?
I and IV Yes
II and V No

Since II and IV have the same slope, they are the same line. Thus, it's only I and IV that are parallel.

b
To tell if two lines are perpendicular, we check if their slopes are opposite reciprocals. This means that their slopes will multiply to

In part A, we found the slopes of each line.

Line Equation Slope
(I)
(II)
(III)
(IV)
(V)

To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals are opposite reciprocals. Thus, let's rewrite the slopes that are whole numbers as reciprocals to find which ones that are opposite.

Line Slope
(I)
(II)
(III)
(IV)
(V)

Since the product equals line III is perpendicular to both line II and V.