Finding the Slope of a LineFind the slope of the line through the points and
We let and in the slope formula.
Thus, the slope is - See FIGURE 15.
47.
m=
y 2 - y 1
x 2 - x 1
=
3 - 1 - 12
- 5 - 2
=
4
- 7
= -
4
7
1 2, - 12 = 1 x 1 , y 12 1 - 5, 3 2 = 1 x 2 , y 22
1 2, - 12 1 - 5, 3 2.
EXAMPLE 1
SECTION 3.2 The Slope of a Line 149
xy0
–5 – 2 = –73 – (–1) = 4(–5, 3)(2, –1)
m = = ––7^447FIGURE 15If we interchange the ordered pairs so that and
in the slope formula, the slope is the same.
m=
- 1 - 3
2 - 1 - 52
=
- 4
7
= -
4
7
1 - 5, 3 2 = 1 x 1 , y 12 1 2, - 12 = 1 x 2 , y 22
NOW TRYExample 1suggests the following important ideas regarding slope:
1.The slope is the same no matter which point we consider first.
2.Using similar triangles from geometry, we can show that the slope is the same no
matter which two different points on the line we choose.
CAUTION In calculating slope, be careful to subtract the y-values and the
x-values in the same order.
Correct Incorrect
or or
The change in y is the numerator and the change in x is the denominator.
OBJECTIVE 2 Find the slope of a line, given an equation of the line.When
an equation of a line is given, one way to find the slope is to first find two different
points on the line and then use the slope formula.
Finding the Slope of a LineFind the slope of the line
The intercepts can be used as the two different points needed to find the slope.
Let to find that the x-intercept is Then let to find that the
y-intercept is Use these two points in the slope formula.
m= NOW TRY
rise
run
=
8 - 0
0 - 1 - 22
=
8
2
= 4
1 0, 8 2.
y= 0 1 - 2, 0 2. x= 0
4 x- y=-8.
EXAMPLE 2
y 1 - y 2
x 2 - x 1
y 2 - y 1
x 1 - x 2
y 1 - y 2
x 1 - x 2
y 2 - y 1
x 2 - x 1
NOW TRY
EXERCISE 1
Find the slope of the line
through the points
and. 1 - 3, 5 2
1 2, - 62
NOW TRY ANSWERS
2.^37
-^115
NOW TRY
EXERCISE 2
Find the slope of the line
3 x- 7 y= 21.
y-values are in the
numerator, x-values in
the denominator.