Section 3­3 Slopes of Lines
­ The slope of a line is the ratio of its vertical rise
to its horizontal run.
slope = __vertical rise_
horizontal run
­ In a coordinate plane, the slope of a line is the
ratio of the change along the y­axis to the
change along the x­axis.
­ The slope of a line indicates whether the line
rises to the right, falls to the right, is horizontal,
or is vertical.
­ The slope of a vertical line is undefined.
1
2
Examples of 4 Situations when finding slope
1.
2.
Line rises from left Lines falls from left to right to right
Positive Slope
Negative Slope
3.
4.
Horizontal Line
Vertical Line
Slope = 0
Ex: Slope = undefined
Ex:
3
Ex 1 Determine the slope of the line that contains the given points.
a. J (0, 0) , K (­2 , 8)
b. R (­2 , ­3) , S (3 , ­5)
c. L ( 1, ­2) , N (­6 , 3)
d. P (­1 , 2) , Q (­9 , 6)
4
Ex 2 Find the slope of each line.
a. AB
b. CD
c. EM
d. AE
5
­ The slope of a line can be used to identify the
coordinates of any point on the line.
Ex 3 Determine the value of x so that a line containing (6 , 2) and (x , ­1) has a slope of .
Postulate 3.2 Two nonvertical lines have the same slope if and only if they are parallel.
Summary: Parallel lines have the same slope!
Postulate 3.3 Two nonvertical lines are perpendicular if and only if the product of their slopes is ­1.
Summary: Perpendicular lines have slopes that are negative reciprocals of one another!
Ex: 5 and
and 6
Ex 4 Determine whether MN and RS are parallel, perpendicular, or neither.
a. M (0 , 3) , N (2 , 4) , R (2 , 1) , S (8 , 4)
b. M (­1 , 3) , N ( 0 , 5) , R (2 , 1) , S (6 , ­1)
c. M(­1, 3) , N (4 , 4) , R (3 , 1) , S (­2, 2)
7
Ex 5 Find the slope of each line.
a. a line parallel to TW.
b. a line perpendicular to NP.
­ The relationship of the slopes of lines can be
used to graph a line parallel or perpendicular to
a given line.
­ Recall that slope = __vertical rise_
horizontal run
8
Ex 6 Graph the line that satisfies each condition.
a. slope = 3, contains A (0 , 1)
b. , contains R (­4 , 5)
c. contains Y (3 , 0), parallel to DJ with D (­3, 1)
and J (3 , 3).
d. contains T (0 , ­2) , perpendicular to CX with
C (0 , 3) and X (2 , ­1).
Assign Pgs. 142 ­ 144 # 15 ­ 38, 42 , 43, 49, 51 ­ 62
9