FIGURE 28shows the graphs of and These lines appear
to be perpendicular(that is, they intersect at a 90° angle). As shown earlier, solving
for ygives with slope. We must solve
for y.
Subtract 2x.
Multiply by.SlopeThe product of the two slopes and 2 is
The product of the slopes of two perpendicular lines, neither of which is vertical, is
always This means that the slopes of perpendicular lines are negative (or oppo-
site) reciprocals—if one slope is the nonzero number a, the other is The table in
the margin shows several examples.
-^1 a.
1.
-
1
2
122 = - 1.
-
1
2y= 2 x- 6 - 1
- y=- 2 x+ 6
2 x-y= 6
- 2 x-y= 6
1y=- 2
1x+ 2 y= 4 2 x+2,
x+ 2 y= 4 2 x-y= 6.
SECTION 3.3 The Slope of a Line 205
Deciding Whether Two Lines Are Parallel or PerpendicularDecide whether each pair of lines is parallel, perpendicular,or neither.
(a)
Find the slope of each line by first solving each equation for y.
Subtract x. Add 3x.Divide by 3.Slope is-. Slope is 3.
1
3y=-
1
3
x+
7
3
3 y=-x+ 7 y = 3 x+ 3
x + 3 y= 7 - 3 x+y= 3
- 3 x+ y= 3
x+ 3 y= 7
EXAMPLE 6
Number Negative Reciprocal, or
, or
, or , or 2.5The product of each number and its
negative reciprocal is 1.
10- 4
4 - 0.4 10
1
6
6
(^61)
(^12) - (^21) - 2
(^34) - (^43)
–3
2
x + 2y = 4
x + 2y = –6
x
y
Parallel
lines
Slope = –
Slope = –
1
2
1
2
–6 0 4
FIGURE 27
Slope = 2
2 x – y = 6
x + 2y = 4
Perpendicular
lines
Slope = –^122
–6
x
y
034
FIGURE 28
Slopes of Parallel and Perpendicular Lines