Download Investigation 6 Rational and Irrational Slopes

Problem of the Day
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Each letter in the equation stands for a different number (0-9).
Look at each equation carefully. Think about what you know
about how numbers work. Find the value of each letter (A-J).
G+G+G=D
J+E=J
G2 = D
B+G=D
F–B=C
I = A; hint: (H > A)
H
AxC=A
Answers to POD
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A=2
B=6
C=1
D=9
E=0
F=7
G=3
H=4
I=8
J=5
Looking for Pythagoras
Investigation 6
Rational and Irrational Slopes
6.1 Revisiting Slopes
Slope
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The slope is the ratio of
the change in the
vertical direction to the
change in the horizontal
direction.
rise
slope 
run
Slopes to Remember
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Positive Slope
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Zero Slope
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Negative Slope
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Undefined (No Slope)
Slopes of Parallel and Perpendicular
Lines
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Parallel lines have
equal slopes.
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Perpendicular lines
have slopes that are
negative reciprocals of
each other.
What is the slope?
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What would be the slope of a line passing
through the origin and the point (1,2)?
slope 
rise 2

run 1
Problem 6.1
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In your groups, work problem 6.1 on page
65.
Answers to Problem 6.1
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Line
OA
OB
OC
OD
OE
OF
OG
OH
OI
OJ
OK
Slope
0
1/7
2/7
3/7
4/7
5/6
6/5
7/4
7/3
7/2
7/1
Writing in Math
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What is the relationship between the
answers in problem 6.1? Explain your
answer.
Problem 6.1 Follow-Up
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Numbers 1-4, pages 65-66.
Problem 6.1 Follow Up Answers
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1a. Possible Answers (14, 4) and (21, 6)
1b. Possible Answers (12, 10) and (18, 15)
2a. Possible Answers (1,1), (2,2), & (3, 3)
2b. The line makes a 45° angle with the
x-axis
3. The slope is the ratio of the rise to the run
4. Rational number because it is the ratio of
two integers
ACE Questions
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Work the following ACE Questions on pages
68-71.
Numbers 4, 8, 9, 15
Summary
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The slope of a line is a rational number, the
ratio of two whole numbers, if it passes
through two points on the grid.