Download 1. Slope of a line

Slope of a line
10.1 Finding slope from
2 pts
and graph
Ordered Pairs will be
(-,+)
(0,0)
Ordered Pairs will be
(+,+)
Also called Horizontal
Axis
Ordered Pairs will be
(-,-)
Ordered Pairs will be
(+,-)
Also called Vertical Axis
Remember how to plot and
read ordered pairs?
Name the
ordered
pairs for M,
N, R, S
Graph points
A(6, -4)
B(0, -5)
C(-3, 1)
D(5, 0)
C
R
S
(1, 2)
D
(-5, 0)
M
(-3, -2)
N
(4, -2)
B
A
3 ways to determine Slope (m)



From an equation – you must solve
for “y” first.
From a line on the graph.
From 2 points – (the slope formula
using two ordered pairs.)
Can’t add or sub
these
Why?
They are not
Like Terms
Solve for Y
2x  4 y  8
2x
2x
4 y  2 x  8
4
4 4
2
8
y
x
4
4
1
y  x2
2




We want y by itself
Move the x term (do
the opposite + or -)
Move the term in
front of y (do the

opposite x or
)
Slope = ½
D
Negative
Slopes
Positive
Slopes
C
B
E
A
Read line from left to right
Going up—positive
Going down--negative
Types of lines
Angles up
Slope is ______
Positive
Angles down
Horizontal
Vertical
Slope is ________
Slope is ______
Slope is _____
Negative
Zero
Undefined
Find slope from a graph
Going up is Positive


right is
left is
Negative
Positive



Going down is Negative
Slope is a fraction
How far did you go
up/down?
Over
How far did you left/right?


rise
up
/
down
Slope =

run left  / right 
Write this
on notes
down 1
1

Slope 

right
3
3
B
Read line from left to right
Going up—positive
Going down--negative
A
up
Slope 
1
right 4
Find slope from a graph
Going up is Positive


right is
left is
Negative

Positive



Going down is Negative
Pick two points on the grid
Starting from left pt, count
up or down on grid
Write down that number in
the numerator
Count left or right to next
point
Write down this number in
denominator
This fraction is your slope
up
3
Slope 

right 1
C
D
4
up
Slope 

right 2
2
down 2
Slope 

right
3
E
up
3
Slope 

right 4
Read line from left to right
Going up—positive
Going down--negative
F
Steps to find slope from 2 pts


(x1, y1) (x2, y2)
(2, 7) (8, 3)

(x1, y1) (x2, y2)


Formula
(it will be given to you)
y2  y1
m
x2  x1
Label your points


Plug points into
formula
Simplify top and
bottom, then divide the
two numbers
Calculator (y2 - y1) divide
(x2- x2) enter
Example 1


m
(x1, y1) (x2, y2)
(0, 4) (1, 2)
24
10
2
m
1
 2
y2  y1
m
x2  x1

Label your points
(x1, y1) (x2, y2)



Plug points into
formula
Simplify top and
bottom, then divide
the two numbers
Calculator (y2 - y1)
divide (x2- x2) enter
Example 2


(x1, y1) (x2, y2)
(7, -4) (9, -1)
1  4
m
97
3
m
2
y2  y1
m
x2  x1

Label your points
(x1, y1) (x2, y2)



Plug points into
formula
Simplify top and
bottom, then divide
the two numbers
Calculator (y2 - y1)
divide (x2- x2) enter
Example 3-4
3)


m
(x1, y1) (x2, y2)
(10, 5) (3, 5)
5  5
3  10
0
m
7
0
y2  y1
m
x2  x1
(x1, y1) (x2, y2)
4) (-4, 2) (-4, 0)
0  2
m
4  4
2  undefined
m
0
0
m
2
0
2  undefined
m
0
All
VERTICAL
lines have
NO SLOPE.
All HORIZONTAL lines
Have a ZERO slope.