LinearFunctionsontheSmartboard.notebook
February 02, 2017
Not Linear
This smartboard lesson is intended for the use with middle school students. Activities have been included to enhance learning and reinforce the lessons. You will navigate this lesson in the slide order using the arrows to navigate. There are several hidden messages that you can tap to discover. If you have any questions feel free to email me at [email protected]. Enjoy!
Linear
Sep 21­11:01 AM
X
Y
0
1
2
3
-3
2
7
12
Sep 8­2:23 PM
You Try!
Tables
Tables
y = 3x + 4
X -1 0 1 2
Y 4 0 -2 -5
y = 6x ­ 5
X
Y
X
Y
Which table
matches the
graphs?
Equations
Equations
3x + y = 1
y = 5x - 3
Sep 21­2:01 PM
What do the
numbers
represent?
Sep 21­3:03 PM
You Try!
Relations
Relations
(3, 8)
tes
rdina
(-8, 7)
Coo
(x, y) Ordered Pairs
(5, 4)
(-3, 4)
Distance
(7, -4)
(3, 4)
(-2, -5)
(-6, -8)
Domain (X)
Range (Y)
Sep 21­3:18 PM
(-6, -2)
Sep 21­3:26 PM
1
LinearFunctionsontheSmartboard.notebook
You Try!
Values
Values
Domain - set of
all input values.
Your x values
Range - set of
all out put
values. Your y
values
February 02, 2017
X
Y
0
-3
y = 5x - 3
X
Y
0
-3
Domain =
y = 5x - 3
y = 5(0) - 3
Range =
y=0-3
y=-3
Sep 22­3:08 PM
Sep 22­3:25 PM
Functions
Functions
Graphs & Functions
~ Exactly one input for
exactly one output
Input(x)
How do we tell
which ones are
functions?
1
2
3
4
Output(y)
23
36
47
61
6
Not Functions
4
2
­6 ­4 ­2
­2
­4
2
4
6
­6
Sep 22­3:26 PM
Vertical Line Test
Vertical Line Test
-1
2
3
4
0
1
2
5
The input 3 has
outputs of 1
and 2
Sep 23­4:03 PM
You Try!
just slide the red bar to test
~if the vertical line crosses
more than 1 point at a time
then it's not a function.
This is a classic
example of a linear
function where for
every input (or x
value) there is
exactly one output
(or y value).
Are these
graphs of
functions?
Sep 23­4:07 PM
So how do we
find out?
Sep 9­10:54 AM
2
LinearFunctionsontheSmartboard.notebook
February 02, 2017
This is a classic
example of a
quadratic function.
You will learn more
about those in
another lesson. This
just shows graphs
other than straight
lines can be
functions, too.
This is not. As you
can see our vertical
line crosses this
graph in several
areas showing us
that the same input
(x) has two outputs
(y)
Sep 9­10:54 AM
Sep 9­10:51 AM
This is not a
function because
our vertical line
test crosses the
graph at two
points.
This graph is not a
function because if
you check all of the
points you will find
that the red line
crosses two of
them at the same
time.
Sep 9­10:57 AM
Linear Equations in Two Variables
2x - y = 5
Checking Solutions
2x - y = 5
?
2(1) - (-3) = 5
5=5
Sep 9­10:51 AM
Y = 4x - 7
X
Y
(1, -3) or (4, 7)
2x - y = 5
?
4
2( ) - (7) = 5
1=5
Sep 28­9:42 PM
Sep 23­7:26 PM
3
LinearFunctionsontheSmartboard.notebook
3x + 4y = 0
3x - y = 5
X
February 02, 2017
X
Y
Y
Sep 23­7:26 PM
x + 2y = 6
X
Sep 23­7:26 PM
Using Intercepts
Y
Y-intercept ~ point where a
graph crosses the y-axis
x-intercept ~ point where a
graph crosses the x-axis
Sep 23­7:26 PM
Y-intercept
x-intercept
Sep 28­9:36 PM
Find the x and y intercepts to graph the equation.
Finding Intercepts
Finding Intercepts
x + 2y = 6
x-intercept
3x - 2y = 6
3x - 2(0) = 6
3x = 6
x=2
y-intercept
3x - 2y = 6
3(0) - 2y = 6
- 2y = 6
y = -3
Sep 28­10:23 PM
Sep 9­12:27 PM
4
LinearFunctionsontheSmartboard.notebook
February 02, 2017
4x + 2y = 15
Sep 9­12:27 PM
5