Finding Slopes of Horizontal and Vertical LinesFind the slope of each line.
(a)
The graph of is a horizontal line. See
FIGURE 16. To find the slope, select two different
points on the line, such as and and
use the slope formula.
In this case, the riseis 0, so the slope is 0.
(b)
The graph of or is a ver-
tical line. See FIGURE 17. Two points that satisfy
the equation are and
We use these two points and the slope formula.
Since division by 0 is undefined, the slope is unde-
fined. This is why the definition of slope includes
the restriction that
NOW TRYExample 3illustrates the following important concepts.
x 1 x 2.
m=
rise
run
=
- 4 - 5
- 1 - 1 - 12
=
- 9
0
x=- 1 1 - 1, 5 2 1 - 1, - 42.
x+ 1 = 0, x=-1,
x+ 1 = 0
m=
rise
run
=
2 - 2
3 - 1 - 12
=
0
4
= 0
1 3, 2 2 1 - 1, 2 2 ,
y= 2
y= 2
EXAMPLE 3
150 CHAPTER 3 Graphs, Linear Equations, and Functions
xy0(−1, 2) (3, 2)y = 2m = 0FIGURE 16xy0(−1, −4)(−1, 5)
x + 1 = 0Undefined
slopeFIGURE 17Horizontal and Vertical Lines- An equation of the form always intersects the y-axis at the point
The line with that equation is horizontal and has slope 0.
- An equation of the form always intersects the x-axis at the point
The line with that equation is vertical and has undefined slope.
x=a 1 a, 0 2.
y=b 1 0, b 2.
The slope of a line can also be found directly from its equation. Look again at the
equation from Example 2.Solve this equation for y.
Equation from Example 2Subtract.
Multiply by.Notice that the slope, 4 , found with the slope formula in Example 2is the same num-
ber as the coefficient of xin the equation We will see in the next sec-
tion that this always happens, as long as the equation is solved for y.
y= 4 x+ 8.
y= 4 x+ 8 - 1
- y=- 4 x- 8 4 x
4 x- y=- 8
4 x- y=- 8
NOW TRY
EXERCISE 3
Find the slope of each line.
(a)y- 6 = 0 (b)x= 4
NOW TRY ANSWERS
- (a) 0 (b)undefined