Unit 7 The Big Race Unit 6

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Unit 7 The Big Race (Unit 6 ½)

• Review Problems from Algebra 1 Part 1
• Simplifying Expressions
• Evaluating Expressions using The Order of
  Operations
• Multiplying Binomials
• Solving Equations
• Guess and Check Word Problems
• Graphing Equations Using a Table

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Unit 7 The Big Race
BR-1 (Resource Page) Leslie rides at a constant
rate of 2 meters per second. On the resource page
provided, neatly graph and write an equation in
terms of x and y that shows the distance Leslie
travels. Let x represent time in seconds and y
represent the distance in meters. Find Leslies
equation and label her line appropriately.
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Unit 7 The Big Race
BR-2 Write a rule using x and y for a line or
curve that uses the following coordinates. Look
for patterns to help find the rule. a) (4, 2),
(8, 4), (-10, -5), (16, 8) b) (1, 6), (4, 9),
(-1, 4), (10, 15) c) (3, 9), (4, 16), (7, 49),
(-2, 4)
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Unit 7 The Big Race
Scaling Axes Before setting up a graph, it is
important to analyze if both positive and
negative numbers are needed. Then you must decide
how to scale the x-and y-axes. On each axis, one
unit of the graph paper must represent the same
increment, but each axis can have different
scales.
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Unit 7 The Big Race
BR-3 SLEEPY TIME An equation used to relate the
age of a person to the number of hours of sleep
required each day is shown, where H represents
the number of hours of sleep required and A
represents the age in years.
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Unit 7 The Big Race
BR-3 SLEEPY TIME a) Graph this equation with H on
the vertical axis and A on the horizontal axis.
What is the smallest and largest number of hours
you will need on this axis? What is the youngest
age? The oldest age? Mark your axes clearly to
reflect these values. Discuss the range of H and
A.
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Unit 7 The Big Race
BR-3 SLEEPY TIME b) Plot the point on the graph
that represents you age and your typical number
of hours of sleep. Are you on the line? Label
each of your study team members on the graph with
their name to see if they are on or off the line.
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Unit 7 The Big Race
BR-3 SLEEPY TIME c) Does this formula work for
you? Does it work for babies? Does it work for
older people? For what ages does the formula seem
to work best? Is there a point on this graph that
makes no sense? Explain.
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Unit 7 The Big Race
BR-4 On graph paper draw and label
ABC
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Unit 7 The Big Race
BR-4 a) Write the ratio of (the vertical
side) (the horizontal side) b) Enlarge
ABC so that the new triangle, DEF, has
corresponding sides twice as long. Draw and label
DEF.
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Unit 7 The Big Race
BR-4 c) Write the ratio of (the vertical
side) (the horizontal side) d) What do
you notice about the ratios for parts (a) and
(c)? e) Use similar figures to justify your
findings about the ratios.
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Unit 7 The Big Race
HW BR- 5-10
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Unit 7 The Big Race
BR-11 Dina wants to see if she could win the Big
Race with a 3 meter head start. If she can ride
her tricycle 1 meter per second, can she beat
Leslie? Using her speed and her head start, add
Dina to your graph on BR-0 resource page. Label
her graph with her name and equation.
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Unit 7 The Big Race
BR-11 a) Compare both Leslie and Dinas lines. b)
How is Dinas head start represented on the graph?
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Unit 7 The Big Race
BR-12 Money Maters Worksheet
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Unit 7 The Big Race
TOOL KITS X- and Y-INTERCEPTS X-INTERCEPT of a
line is the point where the graph crosses the
x-axis, that is, where y 0. To find the
x-intercept substitute 0 for y and solve for x.
Its coordinate is ( x, 0).
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Unit 7 The Big Race
TOOL KITS X- and Y-INTERCEPTS Y-INTERCEPT of a
line is the point where the graph crosses the
y-axis, which happens when x 0. To find the
y-intercept substitute 0 for x and solve for y.
Its coordinate is (0, y).
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Unit 7 The Big Race
BR-14 Find the x- and y-intercepts for the two
lines below and use them to graph each line.
Write the coordinates of x- and y-intercepts on
your graph. a) x 2y 4 b) 3x 6y 24
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Unit 7 The Big Race
BR-15 a) The graph of the equation
2x 3y 7 is a line. Find the x- and
y-intercepts and graph the line using these two
points. b) If a point on this line has a
x-coordinate of 10, what is the
y-coordinate?
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Unit 7 The Big Race
BR-21 Look at Leslies and Dinas graphs on your
BR-0 Resource Page. a) What happens to Leslie and
Dina at the point of intersection? b) Where is
the point of intersection? c) Use substitution
and your equations for Leslie and Dina to verify
your point of intersection.
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Unit 7 The Big Race
BR-22 Comparing Graphs Worksheet Some of the
lines are quite steep others are not. Below each
line there is a ratio that describes how steep it
is. The ratio is called the slope of the line.
With your study team, discuss and compare the
graphs and ratios to discover how to determine
the slope of a line.
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Unit 7 The Big Race

• BR-22 Comparing Graphs
• Describe how to find the slope of a line. If your
  team found more than one method, describe each
  method. Your descriptions should be clear enough
  for other teams to understand.
• B. How can you determine if the slope is positive
  or negative?
• C. Does it matter if the triangle is above or
  below the line? Why or why not?

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Unit 7 The Big Race
BR-23 Slope Triangles Worksheet
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Unit 7 The Big Race
BR-24 Graph each to the following pairs of points
on the graph paper. Draw the slope triangle and
determine the slope. a) (1, 2) and (4, 5) b) (3,
8) and (5, 4) c) (-6, 8) and (-4, 5) d) (7, 3)
and (5, 4) e) (-4, 5) and (5, 4) f) (5, 0) and
(0, 1) g) Jim got 1 for the slope of the line
the line through points (1, 2) (4, -1). Explain
where Jim made his mistake correct it.
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Unit 7 The Big Race
TOOL KITS The Slope of a Line The SLOPE of a
lineis a measure of the rate at which something
changes. It represents both steepness and
direction. slope
vertical change
horizontal change
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Unit 7 The Big Race
TOOL KITS The Slope of a Line slope
change in y-values
change in x-values
Note that lines that go upward from left to right
have positive slope, while lines that go downward
from left to right have a negative slope. Slope
is denoted by m. Also referred to as rise over
run.
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Unit 7 The Big Race
BR-26 Use the scale graph provided of the three
points A (12, 334), B (288, 334), and C (288,
934) to answer the questions.
a) What kind of triangle is ABC? b) What is
distance AB? c) What is distance BC? d) What is
the slope of the Line AC, that contains (12, 334)
and (288, 934)? e) What is the area of the
triangle?
C
B
A
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Unit 7 The Big Race
BR-33 Study these slopes.
a) Which of the slopes above are negative? b)
Which of the slopes above are positive? c) Does
the sign of the ratio depend on the position of
the negative sign? Explain.
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Unit 7 The Big Race
BR-34 Estimate the slope of each line below.
Remember to describe each slope with a positive
or negative ratio.
c)
d)
b)
a)
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Unit 7 The Big Race
BR-35 Graph the line
a) Mentally verify that this line goes through
the points O (0, 0), A (2, 1), B (4, 2), C
(10, 5), D (-6, -3), E (-8, -4),
and F (2000, 1000). Explain how you verified
point F.
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Unit 7 The Big Race
BR-35 Graph the line
b) If you use points A and B to compute the slope
and points A and D to compute the slope, how will
the answers compare? c) Describe how to move
(slide) from the y-intercept to point A.
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Unit 7 The Big Race
BR-36 Match-a-graph (Part 3) Worksheet BP-37
Refer back to RP BP-12 Determine the slope for
each persons line. Determine the y-intercept for
each line. How do these relate the the equations
for each person? Be sure to consider whether the
slope is positive or negative.
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Unit 7 The Big Race
BR-38 Graph the line
a) Mentally verify that this line goes through
the points O (0, 3), A (2, -1), B (3,
3), C (-1, 5), D (-2, 7), E
(1000, -1997). b) Compute the slope of this
line. c) What is the y-intercept of y -2x
3? d) How do the answers from part (b) and (c)
compare with the original equation?
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Unit 7 The Big Race
BR-39 Find the slope of the line
. How did you determine the slope?
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Unit 7 The Big Race
HW BR- 27-32
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Unit 7 The Big Race
BR-47 Dean has decided he will enter the race. He
estimates that he rides 3 meters every 4 seconds
and wants a 2 meter head start. a) On the RP,
graph a line representing Deans distance from
the starting line. Label his graph with his
name. b) How many meters does Dean ride each
second? c) Compare your answer to (b) with the
slope.
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Unit 7 The Big Race
BR-48 On a sheet of graph paper, draw a set of
coordinate axes. Draw a line through the origin
that has a slope of 1. Remember that the origin
is the point (0, 0). a) Write the coordinates of
three points that are on the line. b) Write an
equation that describes these points.
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Unit 7 The Big Race
BR-49 Understanding the Equation of a
Line Worksheet
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Unit 7 The Big Race
BR-50 Without graphing, identify the slope and
y-intercept of the following equations. 1) 2)
3) 4) 5) 6)
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Unit 7 The Big Race
TOOL KITS SLOPE-INTERCEPT FORM Any line can be
described by an equation in the form of y mx
b. The m represents the slope (it is the
coefficient of x). The b represents the y-value
of the y-intercept (where x 0). Ordered pairs
(x, y) that make the equation true are
coordinates on that line.
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Unit 7 The Big Race
Reflection BR-51
HW BR- 53-57
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Unit 7 The Big Race
BR-58 Do you think it is always possible to draw
a line given only one point and its slope?
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Unit 7 The Big Race
BR-59 a) Plot the point (2, 3). b) Draw a line
through that point with a slope of ½. Discuss
with your study team how to do this accurately.
Is there more than one way to do this? c) Find
the equation of the line using the slope and
y-intercept.
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Unit 7 The Big Race
BR-60 Use the slope and the given point on the
line to graph the following lines. Use a ruler
and draw carefully so you can accurately find the
y-intercept for a) A line through (8, 2), with a
slope of ¾. Write the equation of the line. b) A
line through (8, 2), with a slope of -¾. Write
the equation of the line. c) A line through (-4,
3), with a slope of -2. Write the equation of the
line.
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Unit 7 The Big Race
BR-61 Elizabeth and Bob are considering joining
the race. Bob usually rides 3 meters in 2 seconds
and will get a 5 meter head start. Elizabeth
rides 1 meter in 4 seconds and wants a 6 meter
head start. Add lines for Elizabeth and Bob.
Label correctly. a) Who rides faster, Elizabeth
or Bob? How does the graph show this? b) When
does Dean pass Elizabeth? How can you tell by
examining the graph?
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Unit 7 The Big Race
BR-62 Kyle made this sketch to find the slope of
a line through (-15, 39) and (29, -2). Use his
sketch to finish the problem. Remember to check
whether the slope is negative or positive.
y
39
x
29
-15
-2
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Unit 7 The Big Race
BR-63 Draw sketches similar to Kyles to find the
slope of the lines through the given points. We
call this sketch a slope triangle. a) (10, 2) and
(2, 24) b) (-3, 5) and (2, 12) c) (-6, 3) and (2,
10)
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Unit 7 The Big Race
HW BR- 64-69
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Unit 7 The Big Race
TOOL KITS SUBSTITUTION METHOD Given
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Unit 7 The Big Race
BR-72 Use substitution to find the point of
intersection (x, y) for each pair of linear
equations below. a) b) c) d) Verify
that your
solutions work for both equations.
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Unit 7 The Big Race
HW BR- 73-78
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Unit 7 The Big Race
BR-79 If Brian starts 3 second late and catches
up with Dina 7 seconds after the race begins, add
Brians line to the graph. a) What is the
x-intercept for Brians line? b) Find Brians
speed.
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Unit 7 The Big Race
BR-80 Simplify the following expressions. a)
1(4x 6) b) (2x 5) c) 4x (5 2x)
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Unit 7 The Big Race
BR-81 Joe learned substitution yesterday and
solved the following system of equations
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Unit 7 The Big Race
BR-81 a) Joe got an answer of y 10 and
x -16. Check his answer. b) Solve the problem
and find the correct answer. c) What did he do
wrong?
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Unit 7 The Big Race
BR-82 Solve the following systems. Remember to
check your solution in both equations to make
sure it is the point of intersection. a) b)
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Unit 7 The Big Race
HW BR- 83-89
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Unit 7 The Big Race
BR-90 Big Race Part 1 BR-91 Big Race Part 2
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Unit 7 The Big Race
HW BR- 92, 94-96
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Unit 7 The Big Race
Review for Test
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Unit 7 The Big Race
HW BR- 98-103