The Slope
of a Line
Focus 7 - Learning Goal #1: The student will understand the
connections between proportional relationships, lines, and linear
equations and use functions to model relationships between quantities.
4
3
2
1
0
In addition to
level 3.0 and
beyond what
was taught in
class, the
student may:
 Make
connection
with other
concepts in
math.
 Make
connection
with other
content
areas.
The student will
demonstrate and
explain the
connections
between
proportional
relationships,
lines, and linear
equations and
use functions to
model
relationships
between
quantities.
The student
will
demonstrate
and identify
proportional
relationships,
lines, and
linear
equations and
use functions
to model
quantities.
With help
from the
teacher, the
student has
partial
success with
level 2 and 3
elements.
Even with
help,
students
have no
success with
level 2 and 3
content.
Finding Slope of a Line
• The method for finding the steepness of stairs
suggests a way to find the steepness of a line.
• A line drawn from the bottom step to the top set
of a set of stairs touches each step in one point.
• The rise and the run of a step are the vertical
and the horizontal changes, respectively,
between two points on the line.
Finding the Slope of a Line
• The steepness of the line is the ratio of
rise to run, or vertical change to
horizontal change, for this step.
• We call the steepness of a line its slope.
Important things
about slope…
•Slope is the change in y over change in x.
•Slope is represented by the letter m
•Vertical line has NO slope (undefined)
•Horizontal line has a slope zero (0)
Formula for slope:
y 2  y1
m
x2  x1
Find the slope of a line passing
through points (-2,4) and (3,6)
y 2  y1
m
x2  x1
6
4
2
m =3 - -2 = 5
Find the slope of a line passing
through points (1,1) and (3,-2)
-2
1
3
m= 3-1 =2
A slope of -3/2 means that or every time y goes
down 3, x moves over 2
Graph and count to check.
Classify lines by
their slope:
y
x
1. A line with a positive slope rises from left
to right (m>0)
2. A line with a negative slope falls
down from left to right (m<0)
y
x
3. A line with a zero slope is
horizontal (m=0) Equation y = 3
y
x
4. A line with an undefined slope is vertical
(m is undefined) YOU CANT DIVIDE BY 0!
y
x
Find the slope by using the graph.
To find the slope,
start with one point
and count up how
many rows it goes
up and count how
many rows it goes
over. Make this a
fraction and reduce
if necessary.
This line goes up 2
and over 1.
The slope is 2/1 or 2.
Find the slope by using the graph.
To find the slope,
start with one point
and count up how
many rows it goes
up and count how
many rows it goes
over. Make this a
fraction and reduce
if necessary.
This line goes down 2
and over 1.
The slope is -2/1 or -2.