Download Lesson 1-2 Slopes of Lines Object. To find the slope of a line and to

Lesson 1-2 Slopes of Lines
Object. To find the slope of a line and to
determine whether two lines are parallel,
perpendicular or neither
The slope of a line is a number representing the
steepness of the line relative to the x-axis. Let
(x1,y1) and (x2,y2) be any two points on a line. The
difference in y values gives the rise and the
(x2,y2)
difference in x values gives the run. The slope is the
ratio of the rise to the run.
m 
y 2  y1
x 2  x1
(x1,y1)
x2 – x 1
y2 – y1
The figures below show lines with a positive slope.
Lines with positive slope rise to the right.
( 5,3)
( 8,3)
(2,0 )
m 
3 0
8 2

(2,0 )
3
6

1
m 
2
3 0
5 2
 1
The figures to the left show lines with a
negative slope. Lines with negative
slope rise to the left.
( 0,3)
( 6,0)
m 
3 0
1
  2
06
Slopes of Parallel Lines
Two non vertical lines are parallel if and only if they have the same slope.
y
(0,5)
1
y  2 x  4
(0,4)
(0,2)
(0,0)
1
y  2 x  2
1
y  2 x
x
Some Important facts about the slope
of a line.
Horizontal lines have a slope of 0 because
y2 – y1 = 0 for all y.
y2 – y1 = 0
slope = 0
( 5,4)
( 9,4)
Vertical Lines
Vertical lines have a slope of 0 because
x2 – x1 = 0 for all x.
(2, 5)
(2, 1)
x2 – x1 = 0
No slope
It should be apparent that no slope is quite
different from having Zero slope.
Example 1
• What are the slope and y-intercept of 7x + 13y = 26
7 x + 13 y = 26
13 y = -7x + 26
13 y
7 x + 26
=
13
13
7 x
y=
+2
13
7 x
The slope is
and the y-intercept is 2.
13
Slopes of Perpendicular Lines
Two lines are perpendicular if and only if their slopes
are negative reciprocals of each other. That is if the
slopes are m1 and m2 then
m1 = - 1 or m1 • m2 = -1
m2
4
y3x
3
y  4 x
Practice Exercises
Find the slope of the line joining the given points.
1.) (0,0),(5,7)___ (2.) (2,-6),(8,-3)_____
Find the slope and the y-intercept of the linear
equation given
3.) 4x + 3y =9 m=___,b=____(4.) 3y = 11x m=__,b=___
Tell which are graphs of perpendicular or parallel Lines.
5.)(a) 3y=5x- 5 (b) y= -3/5 x + 4 (c) 10y = -6x – 7
6.) (a) y= 5/2x – 8 (b) -15x + 6y – 10 =0 (c) 4x+10y = 15
Homework 1-18 pg.11
19-33 odd pp. 12-13