Section 4-1 Extension: The Family of Linear Graphs
Homework:
A
of graphs share at least
the linear family share?
Date:
characteristic. What characteristic do the graphs in
Review from Section 3-2:
The simplest function in the family of linear functions is the
the function is
.
 This
function is also known as the
 Its graph contains
coordinates.
 Its domain and range are
We are going to investigate how changing the parameters
affects the graphs in the family of linear functions.
and
function.
.
and
in slope-intercept form
Activity 1-Changing
in y = mx + b:
Graph these functions: y = x (in pencil), y = x + 4 (in red), y = x – 2 (in blue).
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
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-8
-9
a.) How do the slopes of the graphs compare?
b.) Compare the graph of y = x + 4 and the graph of y = x. How would you obtain the graph of y = x + 4
from the graph of y = x?
c.) How would you obtain the graph of y = x – 2 from the graph of y = x?
Conclusion: Changing the y-intercept,
the
.
Changing
, translates, or moves, a linear function
in y = mx + b affects the graph in a different way. First, investigate
values of m.
Activity 2-Changing
in y = mx + b (Positive Values):
1
Graph these functions: y = x (in pencil), y = 2x (in red), y = 3 𝑥 (in blue).
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5
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3
2
1
-9 -8 -7 -6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
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8
9
-1
-2
-3
-4
-5
-6
-7
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-9
a.) How do the y-intercepts of the graphs compare?
b.) Compare the graph of y = 2x and the graph of y = x.
1
c.) Which is steeper, the graph of y = 3 𝑥 or the graph of y = x?
Activity 3-Changing
in y = mx + b (Negative Values):
1
Graph these functions: y = x (in pencil), y = -x (in red), and y = − 2 𝑥 (in blue).
9
8
7
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5
4
3
2
1
-9 -8 -7 -6 -5 -4
-3 -2 -1
0
1
2
3
4
5
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8
9
-1
-2
-3
-4
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-8
-9
a.) How are the graphs with negative values of m different than graphs with a positive m?
b.) Does a negative m change the steepness of the graph?
Conclusion: The steepness is determined by the absolute value of
.
|𝑚|is, the steeper your line will be.
 The
 A
m will change the direction your slope is going, not the
.