1. Slope
8.4C Use data from a table or graph to determine the rate of change or slope and y-intercept

2. Guiding Questions What is another word for slope?
What does a line look like when it has positive, negative, zero or undefined slope?
How do you find the slope from a graph?
What does rise/run mean?
How do you find the slope given 2 points?
How do you find the slope of a table?

3. What is Slope? Slope is defined as the steepness of a line.
Slope is also the rate of change of a line
(change in y)
(change in x)

4. Slope and Rate of Change
When the rate of change is constant, the segments form a straight line (linear). The constant rate of change of a line is its slope.

5. What does the line look like when…
You have positive slope?
You have negative slope?
You have zero slope?
You have NO slope?

6. Slope Mountain Ski Resort T. Merrill 2005 Positive slope,
+ work
Negative slope,
- work
Zero slope is zero fun!
NO slope.
Oh No!!!!
Slope Mountain
Ski Resort
T. Merrill 2005

7. Lets Cheer
Positive,
Negative
Zero NO
X-Axis
Y-Axis
Go, Go, Go

8. What Type of Slope is Shown?
Positive Slope
Negative Slope
Zero Slope
No Slope/Undefined

9. Slope of a Graph
When slope is positive or negative we need to find the actual value of the slope or rate of change
On a graph we find slope using the formula
How far up or down it changes
How far left or right it changes

10. Slope of a Graph First pick two points on the line
The points need to be where the lines cross so they are integers
2. Then find the rise and run
3. Determine if the slope of the line is positive or negative
Rise = 2
Run = 3

11. Slope of a Graph First pick two points on the line
The points need to be where the lines cross so they are integers
2. Then find the rise and run
3. Determine if the slope of the line is positive or negative
Rise = 10
Run = 2

12. Slope of a Graphed Line Find the slope of each line belowx y
Slopes:
Find the slope of each line below 4 4

13. Slope of line through 2 points
To find the slope of a line through 2 given points we use the formula
For example, Find the slope of a line that goes through (-3, 5) and (2, 18) -3 5 18 2 X1 y1 X2 y2

14. Given two points on a line, find the slope:
1. (9, 2), (8, -7) X1 y1 X2 y2
2. (-4, 4), (-7, 2) y1 X2 X1 y2
3. (5, -1), (9, -4) X1 y1 y2 X2

15. Given two points on a line, find the slope:
4. (5, 2), (1, 0) X1 y1 X2 y2
5. (3, -3), (3, -1) y1 X2 X1 y2
Undefined, NO slope
6. (-4, -2), (4, -2) X1 y1 y2 X2

16. If it is linear it will be the same no matter which two rows you pick
Slope of a Table
In a table we can use the same formula. Pick any two pairs in the table for coordinates
Pick any two rows.
If it is linear it will be the same
no matter which two rows you pick x y -4
-17 1 -2 3 4 8 19 10 25 x1 y1 x2 y2

17. Slope of a Table Find the slope for each table below x y -3 4.25 -1
2.75 2 1
1.25 5
-1.75 x y -8 2 -6 3 -3
4.5 -1
5.5 6

18. Slope of a Table Find the slope for each table below x y -10 17 -5 10
4.4 5 -4
-11 x y -3 -8 -1 1 4

19. Conclusion Slope is: Describe the slope of each of the following
the rate of change of a line
Undefined/ No slope
Positive slope
Negative slope
Zero/0 slope

20. Guiding Questions (you should be able to answer)
What is another word for slope?
What does a line look like when it has positive, negative, zero or undefined slope?
How do you find the slope from a graph?
What does rise/run mean?
How do you find the slope given 2 points?
How do you find the slope of a table?