(b)The line through and
y-valueCorresponding x-valueSee FIGURE 23. Again, note that the same slope is
obtained by subtracting in reverse order.
y-valueCorresponding x-value NOW TRYm=
- 2 - 5
- 9 - 12
=
- 7
- 21
=
1
3
m=
5 - 1 - 22
12 - 1 - 92
=
7
21
=
1
3
1 - 9, - 22 1 12, 5 2
202 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
CAUTION It makes no difference which point is or Be
consistent, however.Start with the x- and y-values of one point (either one), and
subtract the corresponding values of the other point.
1 x 1 , y 12 1 x 2 , y 22.
(–9, –2)(12, 5)m = = 217 13yx
–4 081244–8FIGURE 23NOW TRY
EXERCISE 3
Find the slope of the line
through and. 1 1, - 32 1 4, - 32
The slopes we found for the lines in FIGURES 22and 23 suggest the following.
Orientation of Lines with Positive and Negative SlopesA line with positive slope rises (slants up) from left to right.
A line with negative slope falls (slants down) from left to right.
Finding the Slope of a Horizontal LineFind the slope of the line through and
Slope 0As shown in FIGURE 24, the line through these two points is horizontal, with equation
y=4.All horizontal lines have slope 0,since the difference in y-values is 0.
m=
4 - 4
- 5 - 2
=
0
- 7
= 0
1 - 5, 4 2 1 2, 4 2.
EXAMPLE 3
–6 –4 –2 0422–24xyy = 4m = 0(– 5, 4) (2, 4)FIGURE 24
NOW TRYNOW TRY ANSWERS
2.
- -^16
NOW TRY
EXERCISE 2
Find the slope of the line
through and
1 - 2, - 42.
1 4, - 52
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