Finding the Slope of a Vertical LineFind the slope of the line through and
Undefined slopeSince division by 0 is undefined, the slope is unde-
fined. The graph in FIGURE 25 shows that the line
through the given two points is vertical with equation
All points on a vertical line have the same
x-value, so the slope of any vertical line is undefined.
NOW TRYx=6.
m=
2 - 1 - 42
6 - 6
=
6
0
1 6, 2 2 1 6, - 42.
EXAMPLE 4
SECTION 3.3 The Slope of a Line 203
NOW TRY
EXERCISE 4
Find the slope of the line
through and
1 - 2, - 42.
1 - 2, 1 2
–2 042–4–22
xym is x = 6
undefined.(6, 2)(6, –4)FIGURE 25FIGURE 26summarizes the four cases for slopes of lines.
Slopes of Horizontal and Vertical LinesHorizontal lines,with equations of the form have slope 0.
Vertical lines,with equations of the form x=k,have undefined slope.
y=k,
yxUndefined
slopePositive
slopeSlopes of lines0
slopeNegative
slope0FIGURE 26OBJECTIVE 2 Find the slope from the equation of a line. Consider this
linear equation.
We can find the slope of the line using any two points on the line. We get these two
points by first choosing two different values of xand then finding the corresponding
values of y. We choose and
Let. Let.
Multiply. Multiply.
Add. Add.The ordered pairs are and Now we use the slope formula.
The slope, is the same number as the coefficient of x in the given equation
It can be shown that this always happens, as long as the equation is
solved for y.This fact is used to find the slope of a line from its equation.
y 3 x5.
3 ,
m=
11 - 1 - 72
- 2 - 4
=
18
- 6
= - 3
1 - 2, 11 2 1 4, - 72.
y= 11 y=- 7
y= 6 + 5 y=- 12 + 5
y=- 31 - 22 + 5 x=- 2 y=- 3142 + 5 x= 4
y=- 3 x+ 5 y=- 3 x+ 5
x=- 2 x=4.
y=- 3 x+ 5
NOW TRY ANSWER
- undefined slope