Find each quotient. See Section 1.8.5 - 1 - 72
- 4 - 1 - 12
- 2 - 1 - 42
3 - 1 - 12
- 3 - 5
2 - 7
4 - 2
8 - 5
PREVIEW EXERCISES
SECTION 3.3 The Slope of a Line 199
OBJECTIVES
The Slope of a Line
3.3
1 Find the slope of a
line, given two
points.
2 Find the slope from
the equation of a
line.
3 Use slopes to
determine whether
two lines are
parallel,
perpendicular,
or neither.
An important characteristic of the lines we graphed in Section 3.2is their slant, or
“steepness.” See FIGURE 17.
xy0Slants up
from left
to rightSlants down
from left
to right
xy0FIGURE 17One way to measure the steepness of a line is to compare the vertical change in the
line with the horizontal change while moving along the line from one fixed point to
another. This measure of steepness is called the slopeof the line.
OBJECTIVE 1 Find the slope of a line, given
two points.To find the steepness, or slope, of the
line in FIGURE 18, we begin at point Qand move to
point P.The vertical change, or rise,is the change
in the y-values, which is the difference
The horizontal change, or run,is the change in the
x-values, which is the difference
Remember from Section 2.6that one way to compare two numbers is by using a
ratio. Slopeis the ratio of the vertical change in yto the horizontal change in x. The
line in FIGURE 18has
To confirm this ratio, we can count grid squares. We start at point Qin FIGURE 18
and count up5 grid squares to find the vertical change (rise). To find the horizontal
change (run) and arrive at point P, we count to the right3 grid squares. The slope
is as found analytically.^53 ,
slope=
vertical change in y (rise)
horizontal change in x (run)
=
5
3
.
5 - 2 =3 units.
6 - 1 =5 units.
xy0Q (2, 1)run = 3 P (5, 6)rise = 5FIGURE 18