SLOPE OF A LINE
8.F.2 COMPARE PROPERTIES OF TWO
FUNCTIONS EACH REPRESENTED IN A
DIFFERENT WAY (ALGEBRAICALLY,
GRAPHICALLY, NUMERICALLY IN TABLES,
OR BY VERBAL DESCRIPTIONS).
SLOPE
Slope describes the slant
or direction of a line.
Given two points (x1, y1) and (x2, y2),
the formula to find the slope of the
straight line going through these two
points is:
y2  y1
m
x2  x1
m  slope
SLOPE
• The subscripts in each ordered pair
indicate that one is a "first" point and
the other is a "second" point .
SLOPE
• Slope also called “rate of change” and
sometimes referred to as “rise over
run“.
• The slope fraction consists of the
"rise" (change in y, going up or
down) divided by the "run" (change
in x, going to the left or right).
X1
Y1
The two points
X 2 Y2
shown are: (0, -4)
and (-3, -6). Now
we have two points
we can put them in
the slope formula:
 6  (4)  2 2
y 2  y1


m
m
3 3
-3-0
x2  x1
EXAMPLE #2
X1
y 2  y1
m
x2  x1
Y1
X2
Y2
(-2,5) (4, - 5)
 5  5  10
5

m

6
4  (2)
3
X1
Y1
X 2 Y2
FIND THE SLOPE: (-3, 6) AND (5, 2)
y 2  y1
m
x2  x1
( 2)  (6)  4 1

m

8
( 5 )  (  3)
2
SLOPE
There are four possibilities for the slope
of a line:
Negative Slope
Positive Slope
y
y
m<0
m>0
x
x
Line rises from left to right.
Line falls from left to right.
HORIZONTAL LINES
The points (-3, 4) and
(5, 4), the slope is:
For every horizontal line, a slope of zero
means the line is horizontal, and a
horizontal line means you'll get a slope of
zero. The equation of all horizontal lines is
of the form y = “a number” (ex. y = 4)
VERTICAL LINES
Now consider the vertical
line of the equation x = 4:
A vertical line will have no slope, and “the
slope is undefined" means that the line is
vertical. The equation of all vertical lines is
of the form x = “a number” (ex. x = 4).
SLOPE
The other two possibilities for the slope
of a line:
Zero Slope
Undefined Slope
y
y
m is undefined
m=0
x
x
Line is horizontal.
Line is vertical.
FIND THE SLOPE OF A LINE THAT
CONTAINS POINTS: (5, 4) AND (5, 2).
y 2  y1
m
x2  x1
( 2)  ( 4)

2
m

(5)  (5)
0
This slope is undefined.
y 2  y1
m
x2  x1
29 7
m

11  3
8
Red
FIND THE SLOPE
X1 Y1
(3, 9)
X
X 22 Y
Y22
Blue
2  ( 2) 2
m

11  5
3
Green
 11

2
(11, 2)
X12 Y12
(5, -2)
Are we going
too fast?
Let’s review!
The mathematic al term to describe
steepness is slope.
Vertical Change (rise)
Slope 
Horizontal Change (run)
Q&A
If I am given a line on the
coordinate plane, how do I find
the slope?
• Pick any two points on the line
and use the slope formula
OR
• Find the “rise” (change along
the y-axis) and the run (change
along the x-axis.
Q&A
If I pick two different points
than someone else won’t I
get a different answer?
•No, the math will be
different, but the answer
will be the same.
(5,6)
(-4,-2)
First pick any two points on the line.
Then find the coordinates of the points
and use them in the slope formula.
KEY SKILLS
1000
Graph the points
(0, 400), (15, 250)
Does the direction
of the line show a
positive or negative -20
trend?
500
10
-10
-500
Negative.
-1000
Find the slope.
y
20
x
KEY SKILLS
TRY THIS
Edgar deposited $100 in the bank. After 6 weeks he
had deposited a total of $220. Graph the amount of
money he has in his account, then find the slope.
What are the 2 sets of (x, y) coordinates?
(0, 100)
(6, 220)
TRY THIS
KEY SKILLS
y
250
Graph the points
(0, 100), (6, 220)
Does the direction
of the line show a
positive or negative -10
trend?
125
5
-5
-125
Positive.
-250
Find the slope.
10
x
KEY SKILL
.m = y2 – y1
x2 – x1
Label the
coordinates
Substitute
into the
formula
(0, 100) ( 6, 220)
x1 y1
x2 y2
m = 220 – 100
120
= 20
=
6
6 - 0
The slope = 20