Cornell Notes
ELL Math
Teacher: Caminero
Name: ________________________
Period: _______Date: ____________
CLOs
TOPIC: Slope of a line
1- Define slope. 2- Identify if the slope is positive, negative, zero, or undefined. 3- Find
the slope of a graphed line. 4- Find the slope with function table. 5- Memorize the
formula to calculate the slope with ordered pairs. 6- Recognize three types of function
forms. 7- Identify the slope in a given equation written in slope-intercept form.
the measure of how
steep or inclined a
line is.
What is slope?
inclination
SLOPE of a line
tendency
lean:
_____________________________________________________________________________
The slope of a graphed line is what says how inclined the line is.
A positive slope means
the right side of the line
points UP.
A negative slope means
the right side of the line
points DOWN.
leaning against:
A horizontal line
has a slope of zero.
A vertical line has
an undefined slope.
(line leans against
the floor)
(line does not lean
against anything)
What symbol do we use for SLOPE in an equation?
_____________
Give an example of an equation: ______________________________________
This is a common equation in algebra:
___________________________________
Many times the equations start with the letter
When an equation starts with
Y.
Y is very easy to identify the slope.
measured:
FINDING THE SLOPE OF A GRAPHED LINE
staircase:
Slope,
1)
2)
steps:
m , is measured using steps, just like on a staircase:
Create a triangle “step” between two points on the line.
Select two points and travel from one point to the other
using up or down movements first. Then, go right or left
until you arrive to the other point.
:
height:
width:
Slope,
m
=
m , is a FRACTION.
 y
=
 x
What is the slope of the line above?
rise
run
=
m , of the line in the graph
here:
y2  y1
x 2  x1
=
slope 
______________ = _____
length:
You try: Find the slope,
depth:
Write the slope as a fraction.
rise:
run:
numerator:
denominator:
_____
y2  y1
FIND THE SLOPE BETWEEN TWO POINTS USING x  x
2
1
MEMORIZE!
y2  y1
x 2  x1
This is the formula
to find slope when
you know the
location of two
points.
 2, 5
Find the slope of the line through
You try: Find the slope of the line through
 7, 11
and
 12, 5
 6, 11
and
FINDING THE SLOPE FROM A TABLE OF VALUES
Slope is sometimes called “rate of change”.
Example: What is the rate of change of air humidity as temperature changes in the table
below?
Humidity (%)
Temperature (˚F)
40
20
45
40
50
60
55
80
What is a function?
Functions are equations that describe how the “ x ” and “ y ” variables work together.
There are three types of functions you must know!
There are three important formats in which functions can be presented.
For example, below is the exact same function, presented in three different forms:
y  2x  7
slope-intercept
form
y  1  2  x  3
point-slope
form
2x  y   7
standard
form
What is the SLOPE of a function in function form?
What is the
coefficient of 3x?
The slope of a function form equation IS the coefficient of the “X”.
What is the
coefficient of -5x?
This is a very important equation you must remember!
y = mx + b
What is the
coefficient of x?
Examples:
3) What is the slope of each function below?
What is the
coefficient of –x?
y  3x 1
slope: ______
y
2
x6
5
slope:_______
y
y  17  3 x
slope: _______
1
x 6
2
slope: ________
What is the
coefficient of 
1
x?
3
State the form of each function below. If the function has no form, write “none.”
2.
form:
form:
form:
form:
_______________
______________
________________
_________________
5. x  y  3
6.
7. 5 y  12  6 x
8.
form:
form:
form:
form:
_______________
_______________
y  3x  5
y  11 x  2
3.
y  2  9  x 1
1. 2 x  7 y  14
4.
________________
2 x  10  y
yx
________________
9. What is the slope of each function below?
y   9x  3
slope: ______
y
2
x2
7
slope:_______
y  1  5x
slope: _______
y
1
x  11
4
slope: ________
State if each graph below has a positive slope, negative slope, slope zero, or
undefined slope.
1What are parallel
lines?
Draw a pair of
parallel lines.
What are
perpendicular lines?
Draw a pair of
perpendicular lines.
Circle the answer:
Which lines never
INTERSECT?
Slope is __________________________
2-
Slope is __________________________
3Slope is __________________________
4Slope is __________________________
5Slope is __________________________
a) parallel
b) perpendicular
Draw a pair of
intersecting lines
that do not form
90° angles.
6-
Slope is __________________________
7Slope is __________________________
Name _____________________
Guided Practice
1- Match each function on the left to its appropriate graph on the right.
______ 1. y 
1
x3
2
______ 2. y 
1
x
2
______ 3. y  
1
x3
2
______ 4. y  
1
x
2
A.
B.
D.
C.
E.
F.
______ 5. y  3 x  2
______ 6. y   3 x  2
2- State the form of each function below. If the function has no form, write
“none.”
1. y  4  6  x  7 
2.
form:
form:
x  3y  1
3. x  4  8 y
form:
________________
_________________
________________
5. y  2 x
6.
7.
form:
form:
_________________
________________
1
x 9
2
form:
_________________
x y 0
4. y 
y 16  x
form:
_______________
8. y  3  x  1
form:
________________
3-
In each coordinate plane below,
a) slope = 0
b) positive slope
draw a line with the indicated slope.
c) undefined slope
d) negative slope
4- Calculate the slope, m of the line that passes through the given pair of points.
a.
 6, 5
and
 2, 13
b.
 3, 1
and
 2, 0
c.
5,  4
5- Write TRUE or FALSE.
__________a. These lines are parallel:
__________b. These lines are parallel:
__________c. These lines are perpendicular because they form angles of 90° :
and
12, 10
6- Calculate the slope,
fraction form.
a.
m
of each line in the graphs below. Write the slope in
c.
b.
m=
d.
m=
e.
m=
m=
f.
m=
m=
Answer these questions:
1-
Define SLOPE: _________________________________________________
______________________________________________________________
2-
What are parallel lines? ___________________________________________