1. Meaning of Slope
Sima Javaheri
&
Sara Kelly

2. California Content Standard
• 3.3 Graph linear functions, noting that the
vertical change (change in y- value) per
unit of horizontal change (change in x-
value) is always the same and know that
the ratio ("rise over run") is called the
slope of a graph.

3. NCTM Standard
• Represent, analyze, and generalize a
variety of patterns with tables, graphs,
words, and, when possible, symbolic rules

4. Objectives of the Lesson
• Given a graph of a line, students will be
able to identify the slope as being positive,
negative, zero, or neither.
• Given a graph of a line, students will be
able to calculate slope by using rise over
run.
• Given a two points on a line, students will
be able to apply the slope formula
accurately.

5. What is Slope???
Slope is the ratio of the vertical change to the
horizontal change. In a linear relationship, it is
a constant rate of change. It can also be
characterized as the steepness of a line.
vertical change rise y2 − y1
slope = m = = =
horizontal change run x2 − x1

7. Positive vs. Negative Slopes
• A line that moves upward from left to right
has a positive slope.
Hint: If you can transform the line to resemble a
“P” then it is positive!
• A line that moves downward from left to
right has a negative slope.
Hint: If you can transform the line to resemble a
“N” then it is negative!

8. Kinds of Slopes
• Positive Slope
• Ne gative S lope

9. Zero and Neither Slope
A line that is flat from left to right has a
zero slope.
A line that is straight up and down (vertical)
has no s lope (neither).

10. Continued
• Zero
• Neither

11. Rise over Run
rise
Slope =
run
Rise is the vertical distance between the points
Run is the horizontal distance between the
points

12. Use Rise over Run
•What is the rise
value? Rise = 4
•What is the run
value? Run = 1
What is the
Slope?
rise 4
= =4
run 1

13. Slope Formula
• Given two points ( x1 , y1 ) and ( x2 , y2 ) , the
slope can be calculated by substituting the x-
and y-values into the following formula:
y 2 −y1
m=
x2 −x1

14. Example
Find the slope of the line that goes
through these two points (1, 1) and (2,3):
3 −1 2
m= = =2
2 −1 1

15. Now, you try…
Given (0,4) and (2, -2), compute
the slope using the slope formula:
−2 −4 −6
m= = = −3
2 −0 2

16. References
1. Kaplan, Andrew. Math On Call. Wilmington:
Houghton Mifflin, 1998.
1. Van de Walle, J, & Lovin, L, Teaching Student
Centered Mathematics, Boston: Pearson (2001).
2. http://www.math.iupui.edu/~momran/m119/notes/slope