1. The Slope of a Line

2. What is Slope?

3. Mountains have slopes….

4. …and so do lines.

5. A skier can go down this slope

6. When you think of down, you think of negative.
y = –x + 6
This line, like the mountain, has a negative slope

7. You can also run up the mountain.

8. When you think of up, you think positive.
y = x – 4
This line, like the mountain, has a positive slope.

9. Does this mountain have a slope??
Slope?? This has
zero slope!

10. Horizontal lines have a slope of zero.
Y = 3

11. What do you think the slope of a vertical line would be ??
This is not a slope; it’s a cliff!
The slope of a vertical line is undefined!
It has NO slope.
X = -5

12. A line that goes up from left to right has what kind of slope???
POSITIVE

13. What kind of line has a slope of zero??
HORIZONTAL

14. What is the slope of this line??
UNDEFINED

15. One more time…. + -
undefined

16. What is Slope? Slope measures the “steepness” of a line.
Slope can be Positive or Negative or Zero (0) or Undefined.
Higher slope values have steeper slopes.

17. y = x + 1
y = x – 4
y = 4x
y = –x + 6
y = 2x + 3
y = –3x + 8

18. Positive Slope
Lines with Positive Slope rise from left to right, appearing to go uphill.
Notice the “m” value is positive.
The larger the value, the steeper the line.
y = x + 1
y = 4x
y = 2x + 3

19. Positive Slope x -2 3 4 8 y -1 1 5 9 x -4 -1 2 3 6 y -5 1 7 9 15
y = 2x + 3
y = x + 1 x -1 1 2 10 y -4 4 8 40
y = 4x
Lines with Positive Slope also have the following relationship between x and y.
As x-values increase, y-values also increase.

20. Negative Slope
Lines with Negative Slope fall from left to right, appearing to go downhill.
Notice the “m” value is negative.
The larger the absolute value, the steeper the line.
y = –x + 6
y = –3x + 8

21. Negative Slope x
− 3 1 3 5 7 y 9 −1 x 2 5 6 10 y 8 −7
−10
−22
y = −x + 6
y = −3x + 8 x −4
− 2 2 4 y 8 −8
y = − 2x
Lines with Negative Slope also have the following relationship between x and y.
As x-values increase, y-values decrease

22. Zero Slope Lines with a Zero Slope are flat (horizontal).
Notice the “m” value is 0 x -2 -1 1 2 y -3
Y = -3

23. Undefined Slope Lines with a Undefined Slope are (vertical).
The equation is an “X” equals equation.
There is no “Y” in the equation. x 4 y -2 -1 1 2
X = 4

24. Slope Of A Line ( 1 , -4 ) ( -2 , 3 ) m = rise run = change in y
change in x
y2 - y1
x2 - x1
If you are given two points…how do you find the slope?
( 1 , -4 ) ( -2 , 3 )

25. What do you think?
Find the slope of the line that passes through the points (-2,-5) and (4,3).

26. So what about the slopes of these lines?
Try this one… (3 , 6) and (3 , -7)
What do you notice?
And this one… (-2, 4) and (0, 4)

27. Memory Device
Zero on top = 0
Zero on bottom = undefined
Oh No!!!

28. The Slope Ratio vertical rise slope = horizontal run so 10 2 2 slope =5 1
Remember to always
simplify the ratio.
horizontal run = 5

29. Let’s Try It Out!
Let’s try and find the slope of a hill that has a vertical rise of 40ft and
a horizontal run of 200ft. Let m represent the slope.
vertical
rise = 40 ft
horizontal run = 200 ft
Don’t touch that button unless you have
tried it on your own first! S
Click the green solution
button to check your
own work

30. Solution: 40 ¸ Apply the formula- vertical rise to horizontal run
Vertical rise = 40 ft
40 ft. 1 40 =
200 ft. 5
Horizontal run = 200 ft
Find the GCF 1
The slope of the hill is 5
back
forward

31. . . The Slope Of A Line (x2, y2) y2 - y1 (x1, y1) x2 - x1
The slope m of a line that passes through
the points (x1, y1) and (x2, y2) is
m =
rise
run =
change in y
change in x
y2 - y1
x2 - x1

32. . . USING A COORDINATE PLANE TO FIND SLOPE
The coordinates are (2,2) and (6,5) y
Use the formula: . 7
rise
5 - 2 3 = = .
run
6 - 2 4 5 3 1 -1 1 3 5 7 -1

33. There are 4 types of Slope
1. Positive Slope
A line that rises from left to right
A line falls from left to right
2. Negative Slope
3. Zero Slope
The line is horizontal
4. Undefined Slope
The line is vertical

34. It’s your turn: Problem # 1 Problem # 2 Problem # 3
Use a piece of graph paper to help you illustrate the slope
Problem # 1
(x , y ) 1
= (1,0) and
(x , y ) = (3, 4) 2
Problem # 2
(x , y ) 1
= (0, 9) and
(x , y ) = (4, 7) 2
Problem # 3
(x , y ) 1
= (1, 2) and
(x , y ) = (5, 2) 2

35. . . Problem # 1 (x , y ) = (1, 0) and (x , y ) = (3, 4) m = y - x m =2 1 3 5 7 y -1
m = y 2 1 - x .
m =
4 - 0
3 - 1 .
m = 4 2
The slope of the line is 2

36. . . Problem # 2 (x , y ) = (0, 9) and (x , y ) = (4, 7) m = y - x m =1
= (0, 9) and
(x , y ) = (4, 7) 2 . . 1 3 5 7 y -1
m = y 2 1 - x
m =
7 - 9
4 - 0
m = -2 4 or -1 2
The slope of the line is -1 which makes it
a negative slope. 2

37. . . Problem # 3 (x , y ) = (1, 2) and (x , y ) = (5, 2) m = y - x m =7 y -1
m = y 2 1 - x . .
m =
2 - 2
5 - 1
m = 4 or
The slope of the line is zero which makes it
a zero slope.

38. WHAT IS THE FORMULA FOR SLOPE OF A LINE?
Let’s Review
There are 4 types of slope
positive slope
negative slope
zero slope
undefined slope
Slope is the steepness of a line
It is described by a ratio of rise to run
A coordinate plane can be used to find the slope of a line
WHAT IS THE FORMULA FOR SLOPE OF A LINE?