The document provides instruction on calculating and interpreting slope. It defines slope as the ratio of rise over run between two points on a line. It gives the formula for calculating slope as the change in y over the change in x between two points. Several examples are worked out step-by-step to demonstrate calculating slope from graphs and point pairs. Key concepts covered include identifying horizontal and vertical lines that have slopes of 0 and undefined respectively.

1.  Warm - Up; Khan Topic
 Continue Slope Practice
 Slope - Intercept Formula

2. Interpreting Graphs of Linear
and Non-Linear Functions

4. nonlinear
1
1pi
1 0
<
Linear/ Nonlinear

5. Given this,what are the x and y axes?
faster
16
7
twice

6. • Find the range of the function below when the domain is {-4, -1, 3}
y = |x| - 2
Warm Up/Test Review
4
𝟏
𝟑
0 0 -13

8. x
y
x2 – x1
y2
– y1
change
in y
change in x
The slope of the line passing through the two points (x1, y1) and
(x2, y2) is given by the formula
(x1, y1)
(x2, y2)
x2 – x1
The rise is the difference of the
y-values of two points on a line.
The run is the difference in the
x-values of two points on a line.
The constant rate of change of a straight line is called the slope.
The Slope of a Line:
Slope is usually represented by the
letter m (from the French, monter,
which means “to go up”).
Straight Lines (linear functions) are straight because
the slope never changes!!

9. (3, 2)
(–1, –2)
Then count horizontally to a second point to find the run.
Count vertically from any one point on the line to find the rise.
Finding the Slope of a Line
slope =
𝟒
𝟒
= 1
The slope of the line is 1.
It does not matter which ordered pair you start with.
slope =
−𝟒
−𝟒
= 1
4
4

10. (5, 4)
Then count horizontally to a second
point to find the run.
Count vertically from any one point
on the line to find the rise.
slope =
𝟐
𝟒
=
𝟏
𝟐
The slope of the line is
𝟏
𝟐
slope =
−𝟐
−𝟒
=
𝟏
𝟐
Find the slope of the line:
It does not matter which y you
begin from.
(1, 2)
The Slope of a Line
The slope of a line is the ratio of rise
to run for any two points on the line.
change in y
change in x
Rise
Run
=

11. Find the slope of the line passing through the points (2, 3) & (4, 5).
The x1 and y1 must come from the same ordered pair.
y2 – y1
x2 – x1
m =
5 – 3
4 – 2
= =
2
2
= 1
2
2(2, 3)
(4, 5)
x
y
The Slope of a Line
Name one other
ordered pair on
this line.

12. The Slope of a Line
What is the slope
of this, and all
horizontal lines?
Don't guess, just
plug the numbers
in...
All horizontal
lines have a slope
of zero.

13. The Slope of a Line
What is the slope
of this, and all
vertical lines?
All vertical lines have a
slope that is undefined
because... a denominator
cannot be zero.

14. m = 0
m = 2
m is
undefined
m =
1
2
m = -
1
4
y2 – y1
x2 – x1
m =
The Slope of a Line

15. The Slope of a Line

16. What is the slope of the line?
The Slope of a Line
Find the next point in
both directions

17. Find the slope of each line:
23
m =
𝟏
𝟐
m = 𝟐m = - 𝟐
1

18. Grand Prix Go-Carts:
What is the y-intercept?
What are the independent (x) and
dependent (y) variables?
How does each change in the x variable affect the dependent,
y variable? In other words, what is the rate of change?
Which graph shows the price function?

19. Test Review:
A
B
C
D
E

20. Is this graph a function?
By what percent did the price of silver drop
between Aug. 7th & August 9th? 36%
Test Review: