Download Lesson 6 changes to b

Objective
SWBAT
describe what
happens to a graph
given a change in yintercept. (A.6C)
DOL
Given
4 equations, students
will correctly predict what
will happen given a change in
y-intercept 3 times. (75%
mastery).
Warm up 11/19/14
1. Graph the equation y= 3x + 2
2. Graph the equation from number 1 if the slope
is changed to -3.
3. What effect did this change have on the xintercept?
4. What would be the new equation of the line
y= 3x + 5 if the slope is multiplied by -10?
Announcements
• Homework due THURSDAY
• Binder Check FRIDAY
• Quest on FRIDAY
• Class work wkst 1-8 due Tuesday, Nov 25th
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• Today after school!
Tutoring
Morning
(8:05 – 8:40 AM)
Afternoon
(4:15 – 4:45 PM)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
9AM–NOON,
Extra Credit Examples

Art:
Music??
http://www.youtube.com/watch?v=SV_s0Q48R6c
http://www.youtube.com/watch?v=s1c3MARlJ0Q
 New

Whiteboard- Rapid Fire!



Designed to be quick.
No talking
Answer the question and hold up your board.
Whiteboards!
 Identify
the y-intercept of the equation
 𝑦 = 9 − 3𝑥
Whiteboards!
 The
slope is always found in front of the
_____.
Whiteboards!
 Identify
the y-intercept of the equation
 𝑦 = 9𝑥 − 3
Whiteboards!
 Identify the slope
1
𝑦 = − 𝑥+9
4
of the equation
Whiteboards!
 Identify
the m of the equation
𝑦 = 7 −𝑥
Whiteboards!
 Identify
the b of the equation
 𝑦 = 18 + 60𝑥
Whiteboards!
 Identify
the y-intercept of the equation
 𝑦 = 100 − 40𝑥
Whiteboards!
 Identify
the slope of the equation
 𝑦 = .33𝑥 + 20
Goal
SWBAT describe the effects
of changing y-intercept (b)
on the graph of a linear
equation
Our Goals This Week:
HW
90%
Why This Matters
Yesterday we looked at changing
slope on a graph, today we look at
the y-intercept. Changing slope and
y-intercept in a “real world”
situation (we will look at next week)
could have drastic effects on bills,
paychecks, or stat lines!
Graph the following (2 mins)
3
Graph the following (2 mins)
3
1, 3, 2
Example 1


A. y = ½x + 1
B. y = ½x – 2
-3
translated down by
Graph “a” was _______
3
____
units to create graph “b”
Let’s look at the equations.
A. b = 1
1 + -3 = -2
B. b = -2
Example 1


A. y = -x + 4
B. y = -x – 4
translated down by
Graph “a” was _______
8
____
units to create graph “b”
Let’s look at the equations.
A. b = 4
4 + -8 = -4
B. b = -4
-8
Essential Vocab
Essential Vocab
Parent
Function
Parallel
Lines
intersect
slope
translation
Shift
Move left or right
Explore Via Desmos! VIVA LA DESMOS
Exploration:
1.
What is the equation of the given line?
________________________________
2.
=
Graph the following equations on the same graph.
1
4
+3
=
1
4
+
=
1
4
−2
=
1
4
−4
3.
What is different about all of the equations given?
4.
What is different about all of the lines?
Explore Via Desmos! VIVA LA DESMOS
Exploration:
1.
What is the equation of the given line?
𝟏
Y= 2 + 𝟒x
________________________________
2.
=
3.
Graph the following equations on the same graph.
1
4
+3
=
1
4
+
=
1
4
−2
=
−4
What is different about all of the equations given?
The y intercepts
4.
1
4
What is different about all of the lines?
They all cross at different points
on the y-axis
Match it up!
Match it up!
F
E
B
C
D
A
Whiteboard Practice
Describe
howofthe
graph
of y= 2xchange
– 1 would
change
if the 1 is with
replaced
e how
the graph
this
line would
if the
1 is replaced
a 7. with
Graph both on either your board or calculator.
𝑦 = 2𝑥 − 1
w Equation: ___________________________
O.E. (original
Equation)
_________________
planation
of how the
line changes:
N.E. (new equation) ___________________
____________________________________
____________________________________
____________________________________
____________________________________
a 7.
Graph both lines to support your answer:
Whiteboard Practice
ribe how the graph of this line would change if the 1 is replaced with a 7.
What would be the equation of a line if the line y=2x + 8 was shifted down by 9
units?
𝑦 = 2𝑥 − 1
Graph both lines to support your answer:
New Equation: ___________________________
Explanation of how the line changes:
O.E. (original Equation) _________________
____________________________________
N.E. (new equation) ___________________
____________________________________
____________________________________
____________________________________
Whiteboard Practice

What would be the equation of the line below if it was
translated down 5 units and then up 8 units?
O.E. (original Equation) ________________
N.E. (new equation) ___________________
Whiteboard Practice

If the graph of the line y=2x +7 is shifted 5 units up, what
would be the new equation?
O.E. (original Equation) ________________
N.E. (new equation) ___________________
Whiteboard Practice
1.
Graph each line to support your answer.
Jose graphed the line of the equation 𝑦 = 5𝑥 + 2. Sarah
graphed the line of the equation 𝑦 = 5𝑥 − 2 on the same
coordinate plane. Which of the following statements best
describe the line that Sarah graphed?
A. It intersects Jose’s line at the point (2, -2).
B.
It is parallel to and 4 units above Jose’s line.
C. It is parallel to and 4 units below Jose’s line.
D. It is exactly the same line as Jose’s line.
2. The two graphs above are an example of a shift or a __________________. These two lines are
____________________ because they have the same _____________!
Independent Practice




Todays Stamp goal: _7_ 4th Period: 8 stamps
Must do problems 9,10,11
Check work at the board
You may help each other but NO COPYING
DOL
1.If the graph of y=-2x –4 is shifted 6 units up, what is the new
equation?
2. If the line y=3x +5 becomes y= 3x –10, which best describes
the change on the line?
A. It becomes more steep
B. It becomes less steep
C. It shifts up 15 units
D. It shifts down 15 units
DOL, cont.
3.
Consider the equation y=2x +5. If the 5 is changed to a -3,
what would be the effect on the line?
A. It would shift 8 units to the right
B. It would shift 8 units up
C. It would shift 8 units down
D. It would shift 8 units to the left
4. If the graph of the line y= 7x + 4 is shifted 6 units down
and then 2 units up, what is the new equation?
DOL
Directions
•
•
•
•
Work silently
Show as much work
as possible
Flip it over and pack
up SILENTLY when
you’re done
Hand it to me as you
walk out the door
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