1. SLOPE of a Line from 2 Points
SLOPE – the measure of steepness, slant, or tilt of a line
The letter m is used to represent slope in equations

2. SLOPE of a Line from 2 Points
SLOPE – the measure of steepness, slant, or tilt of a line
The letter m is used to represent slope in equations

3. SLOPE of a Line from 2 Points
SLOPE – the measure of steepness, slant, or tilt of a line
The letter m is used to represent slope in equations
SLOPE EQUATION
The slope, m , of a non-vertical line that contains the points P1 ( x1 , y1 ) and P2 ( x2 , y2 ) is :

4. EXAMPLE 1 : Find the slope of the line that contains the points
( 2 , 5 ) and ( -1 , 4 )

5. EXAMPLE 1 : Find the slope of the line that contains the points
( 2 , 5 ) and ( -1 , 4 )
x1 y1
x2 y2

6. EXAMPLE 1 : Find the slope of the line that contains the points
( 2 , 5 ) and ( -1 , 4 )
x1 y1
x2 y2

7. EXAMPLE 1 : Find the slope of the line that contains the points
( 2 , 5 ) and ( -1 , 4 )
x1 y1
x2 y2

8. EXAMPLE 2 :
Find the slope of the line thru the given points.

9. EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula

10. EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula
To count the slope from the graph :
Choose a starting point
Move in a y - direction and count
Move in an x – direction and count

11. EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula
To count the slope from the graph :
Choose a starting point
Move in a y – direction and count
Move in an x – direction and count

12. EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula +5
To count the slope from the graph :
Choose a starting point
Move in a y – direction and count
Move in an x – direction and count

13. EXAMPLE 2 :
Find the slope of the line thru the given points. +2
2 options :
a ) count the slope from the graph
b ) use the slope formula +5
To count the slope from the graph :
Choose a starting point
Move in a y – direction and count
Move in an x – direction and count

14. Find the slope of the line thru the given points.
EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula
P2 ( 3 , 2 )
P1 ( 1 , -3 )

15. Find the slope of the line thru the given points.
EXAMPLE 2 :
Find the slope of the line thru the given points.
2 options :
a ) count the slope from the graph
b ) use the slope formula
P2 ( 3 , 2 )
P1 ( 1 , -3 )

16. SOME hints on slope…
( + ) positive slope :
- always uphill from left to right
- when counting, go up, and then right… OR down, and then left
( - ) negative slope :
- always downhill from left to right
- when counting : go down, then right… OR, up, and then left

17. SPECIAL slopes…
Horizontal lines have zero slope.

18. Horizontal lines have zero slope.
SPECIAL slopes…
Horizontal lines have zero slope.
Y doesn’t change on a horizontal line.
P1 ( -5 , 3 )
P1 ( 2 , 3 )

19. Horizontal lines have zero slope.
SPECIAL slopes…
Horizontal lines have zero slope.
Y doesn’t change on a horizontal line.
When you subtract your y – values in the slope equation, you get zero.
P1 ( -5 , 3 )
P1 ( 2 , 3 )

20. SPECIAL slopes…
Vertical lines have no slope or an undefined slope.

21. Vertical lines have no slope or an undefined slope.
SPECIAL slopes…
Vertical lines have no slope or an undefined slope.
X doesn’t change on a vertical line.
P2 ( 2 , 4 )
P1 ( 2 , -3 )

22. Vertical lines have no slope or an undefined slope.
SPECIAL slopes…
Vertical lines have no slope or an undefined slope.
X doesn’t change on a vertical line.
When you subtract your x – values in the slope equation you get a zero.
A zero in the denominator creates an undefined answer…you can not divide by zero.
P2 ( 2 , 4 )
P1 ( 2 , -3 )

23. Graphing slopes…
EXAMPLE 3 : From the point ( -1 , 3 )
graph a slope of m =

24. Graphing slopes…
EXAMPLE 3 : From the point ( -1 , 3 )
graph a slope of m =
STEPS :
1. Graph the given point

25. Graphing slopes…
EXAMPLE 3 : From the point ( -1 , 3 )
graph a slope of m =
STEPS :
Graph the given point
Plot another point by following the given slope

26. EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m =
Graphing slopes…
EXAMPLE 3 : From the point ( -1 , 3 )
graph a slope of m =
- 2
+ 3
STEPS :
Graph the given point
Plot another point by following the given slope
- negative slope so…down 2, then right 3

27. EXAMPLE 3 : From the point ( -1 , 3 ) graph a slope of m =
Graphing slopes…
EXAMPLE 3 : From the point ( -1 , 3 )
graph a slope of m =
- 2
+ 3
STEPS :
Graph the given point
Plot another point by following the given slope
- negative slope so…down 2, then right 3
- plot your new point