slope_and_linear_eq--section_1.4.ppt

Slope of a Line
Slope basically describes the
steepness of a line

If a line goes up from left to right, then
the slope has to be positive
Conversely, if a line goes down from left
to right, then the slope has to be negative

Definitions of Slope
Slope is simply the change in the
vertical distance over the change in
the horizontal distance
1
2
1
2
x
x
y
y
x
y
run
rise
m
slope









1
2
1
2
x
x
y
y
m



The formula above is the one which we
will use to find the slope of specific lines
In order to use that formula we need to
know, or be able to find 2 points on the
line

If a line is in the form Ax + By = C,
we can use the following formula to
find the slope:
B
A
m 


Examples
   
 
3
1
6
2
1
5
4
6
6
,
5
,
4
,
1







m
m
3
2
5
3
2




m
y
x

Horizontal lines have a slope of zero
while vertical lines have no slope
Horizontal
y=
Vertical
x=
m = 0
m = no
slope

The World Of Linear
Equations
Writing Linear Equations
In Slope-Intercept Form
y = mx + b

If you are given:
The slope and y-intercept
 Finding the equation of
the line in y= mx + b
form. Given: slope
and y-intercept. Just
substitute the “m” with
the slope value and the
“b” with the y-intercept
value.
 Slope = ½ and
 y-intercept = -3
y= mx + b
½
-3
y= ½x – 3

If you are given: A Graph
Find the:
 y – intercept = b = the point
where the line crosses the y
axis.
 Slope = = m =
run
rise
s
x'
in
change
s
y'
in
change
 y – intercept = b = -3
 Slope = = m = ½
y= mx + b
2
over
1
up ½
-3
y= ½x – 3

If you are given:
The slope and a point
 Given: slope (m)
and a point (x,y).
To write equations
given the slope and
a point using Point-
Slope Form.
 Slope =½ and point (4,-1)
½ 4-1
y= ½x – 3
Point-Slope Form
1 1
y y m(x x )
  
1 1
y y m(x x )
  
   
4
2
1
1 


 x
y
 
4
2
1
1 

 x
y
2
2
1
1 

 x
y
-1 -1

If you are given:
Two points
 Finding the equation
of the line in y= mx +
b form. Given: Two
points. First find the
slope (m) and then
substitute one of the
points x and y values
into Point-Slope Form.
1 1
y y m(x x )
  
Point-Slope Form
Point (-2, -4) & Point (2, -2)
Find the:
 Slope = = m = s
x'
in
change
s
y'
in
change
run
rise
 
 






2
2
4
2




2
2
4
2
2
1
4
2

 Slope =½ and point (2, -2)
1 1
y y m(x x )
  
½ -2
2
   
2
2
1
2 


 x
y
1
2
1
2 

 x
y
-2 -2
y= ½x – 3

This powerpoint was kindly donated to
www.worldofteaching.com
http://www.worldofteaching.com is home to over a
thousand powerpoints submitted by teachers. This is a
completely free site and requires no registration. Please
visit and I hope it will help in your teaching.

slope_and_linear_eq--section_1.4.ppt

More Related Content

Similar to slope_and_linear_eq--section_1.4.ppt

Recently uploaded

slope_and_linear_eq--section_1.4.ppt