1. Objective- To find the slope of a line given
Lesson 3.5 Slope of a Line
3:5 Slope of a Line
Objective- To find the slope of a line given
two points. y
Graph y = 2x - 3 x y -3 -2 -1 1 2 3 -9 -7 -5 -3 -1 1 3 x
y = 2x - 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. Objective- To find the slope of a line given
two points.
Slope of a line y
vertical change
Slope (m) =
horizontal change +1 y
Slope (m) = x +2
rise
Slope (m) =
run -2 x -4 +2
Slope (m) = = -4
y-intercept = -3 -2 +1
m = 2
y = 2x - 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. y x Find the slope of the line below. Slope (m) = +1 Slope (m) = +3 +3
rise
Slope (m) =
run +1
Slope (m) = +3 x +3 1 m = 3 +1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. y x Find the slope of the line below. +2 Slope (m) = +3 Slope (m) = +3
rise +2
Slope (m) =
run +3
Slope (m) = +3 +2 x 3 m = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. y x Find the slope of the line below. -1 -1 -1 Slope (m) = Slope (m) =
rise
Slope (m) =
run -1
Slope (m) -1 = +4 x +4 -1 m = 4
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. y x Find the slope of the line below. -4 -4 Slope (m) = Slope (m) = +2
rise
Slope (m) =
run -4
Slope (m) = +2 x -4
= -2 m +2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. y x Find the slope of the line below. Slope (m) = +5 +2 Slope (m) = +2
rise
Slope (m) =
run +5 +2
Slope (m) = +2 +5 x 2 m = 5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. y x Find the slope of the line below. -4 -4 Slope (m) = Slope (m) = +1
rise
Slope (m) =
run -4
Slope (m) = -4 +1 x
= -4 m +1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. y Algebraic Method to Find Slope Given Two Points Slope (m) = y
rise
Slope (m) =
run y
Slope (m) = 2 x
(1,2)
y2- y1
Slope (m) =
x2- x1
2 - -3
Slope (m) =
1 - -2 5
Slope (m) = 1 3
(-2,-3) 5
m = 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. Algebraic Method to Find Slope Given Two Points1 2
Find the slope between (-1,3) and (4,7).
y2- y1 y
Slope (m) = = x
x2- x1
7 - 3
Slope (m) =
4 - -1 4
Slope (m) = 5 4
m = 5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

11. -1 - 6 -7 -2 Algebraic Method to Find Slope Given Two Points
Find the slope between (6,5) and (-1,7).
y2- y1
m =
x2- x1
7 - 5 m =
-1 - 6 2 m = -7 -2
m = 7
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

12. -8 - 4 -12 -1 Algebraic Method to Find Slope Given Two Points
Find the slope between (-8,7) and (4,1).
y2- y1
m =
x2- x1
7 - 1 m =
-8 - 4 6 m =
-12 -1
m = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

13. Slope of Horizontal and Vertical Lines Horizontal Lines Vertical lines
x = -3
y = 2
m = 0
m = undefined y
x = -3 y
y = 2 x x
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

14. Slope of Horizontal and Vertical Lines Horizontal Lines Vertical lines
(-2,2) (1,2)
(-3,2) (-3, -1) y
x = -3 y
(-2,2)
(1,2)
(-3,2)
y = 2 x x
(-3,-1)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

15. -1 - 2 -3 - -3 -3 Slope of Horizontal and Vertical Lines
Horizontal Lines
Vertical lines
(-2,2) (1,2)
(-3,2) (-3, -1) 1 2 1 2
y2- y1
y2- y1
m =
m =
x2- x1
x2- x1
2 - 2
-1 - 2
m =
m =
1 - -2 -3
m =
m = 3
Watch Out!
m = undefined
or there is “no slope”
m = 0
m = 0 for all
Horizontal Lines
m = undefined for
all Vertical Lines
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series