Linear Equations Project Based Learning - Henry County Schools
Name:
Date:
Period:
Linear
Equations
Project
Based
Learning
Finished
Item
Points
Received
Part
I
(15
Points)
Question
1
(5
points)
Question
2
(10
points)
Part
II
(30
Points)
Question
3
(10
points)
Question
4
(10
points)
Question
5
(5
points)
Question
6
(1
point)
Question
7
(4
points)
Part
III
(25
Points)
Concept
Builder
Student
Companion
(25
points)
Part
IV
(15
Points)
Review
of
Linear
Equations
(15
points)
Part
V
(15
points)
Using
Linear
Equations
to
Run
a
Business
(15
points)
Total
Points
Received:
_________/100
Points
Graphing
Linear
Equations
PART
I:
Writing
and
Evaluating
Two
?
Variable
Expressions/Functions
With
your
partners,
write
and
evaluate
two--variable
expressions
corresponding
to
the
following
situations.
Write
your
own
work
on
your
worksheet.
Make
sure
to
define
your
variables!
1.
I
was
SOOO
hungry
last
night
at
the
restaurant!
I
ordered
several
Happy
Meals
and
a
ton
of
sodas.
Each
Happy
Meal
costs
$3.20
and
each
soda
costs
$1.75.
(5
points)
a.
Write
an
expression
or
function
to
show
how
much
money
I
spent.
b.
Evaluate
that
expression
for
the
following:
1.
I
ate
4
meals
and
drank
3
sodas
2.
I
ate
10
meals
and
drank
2
sodas
3.
I
ate
3
meals,
but
didn't
drink
any
sodas.
2.
I
got
my
sister
really
mad
at
me
by
teasing
her!
If
I
teased
her
and
started
running,
and
she
started
running
at
the
same
time
(chasing
me),
then
the
distance
between
us
would
be
my
distance
minus
her
distance.
(Assuming
I'm
a
faster
runner.)
Remember
that
distance
is
equal
to
rate
times
time.
a. So,
if
we've
been
running
for
15
sec.,
write
an
expression
for
the
distance
between
us
given
my
unknown
rate
and
her
unknown
rate.
(5
points)
b. How
much
distance
is
between
us
if:
(5
points)
1.
I
run
13
m/sec
and
she
runs
12
m/sec?
2.
I
run
10
m/sec
and
she
runs
5
m/sec?
3.
I
run
11
m/sec
and
she
runs
11
m/sec?
(What
does
that
mean?)
4.
I
run
10
m/sec
and
she
runs
11
m/sec?
(What
does
that
mean?!)
PART
II:
Graphing
Linear
Equations
by
Using
a
Table
3.
The
Algebra
class
wanted
to
start
a
business
selling
bagels
in
the
entryway
of
the
school
in
the
mornings.
If
they
charge
$0.50
per
bagel,
graph
the
revenue
curve.
(10
points)
Hint:
Revenue
is
how
much
money
you
make
when
you
sell
something.
How
can
you
write
an
equation
that
shows
how
much
money
I
make
if
I
sell
x
amount
of
bagels
for
$0.50
each?
a.
Write
an
equation
that
represents
the
revenue
curve.
b.
Graph
this
equation
on
a
coordinate
plane
by
finding
points
to
graph.
Do
this
on
a
separate
piece
of
graph
paper.
Be
sure
to
use
values
of
x
that
make
sense
for
your
domain,
and
label
your
axis
with
numbers
and
titles,
AND
each
graph
so
I
know
what
graph
pertains
to
which
problem.
X
Equation:
(x,y)
20
40
60
80
100
4.
Now,
the
Algebra
class
wants
to
use
a
graph
to
predict
their
total
costs
associated
with
selling
bagels.
Suppose
that
the
fixed
cost
of
the
business
amount
to
$10
and
that
the
variable
cost
per
bagel
is
$0.25
per
bagel.
(10
points)
a.
Write
an
equation
that
represents
the
cost
curve.
b.
Graph
this
equation
on
a
coordinate
plane
by
finding
points
to
graph.
Do
this
on
a
separate
piece
of
graph
paper.
Be
sure
to
use
values
of
x
that
make
sense
for
your
domain,
and
label
your
axis
with
numbers
and
titles,
AND
each
graph
so
I
know
what
graph
pertains
to
which
problem.
X
Equation:
(x,y)
20
40
60
80
100
5.
On
a
separate
axis,
graph
the
two
lines
on
the
same
coordinate
plane.
Show
each
line
in
different
colors.
What
is
happening
when
your
line
that
represents
revenue
goes
above
your
line
for
cost
of
the
business?
(5
points)
6.
Find
the
point
of
intersection
on
the
graph.
Check
to
make
sure
you
have
the
right
point
by
using
your
graphing
calculator.
(1
point)
7.
What
does
the
point
of
intersection
represent?
(4
points)
PART
III:
Graphing
Linear
Equations
WITHOUT
a
Chart
8.
Complete
the
blanks
in
the
following
four
pages.
Each
question
is
worth
1
point,
and
you
can
use
your
textbook
and
prior
knowledge
to
help
you
fill
in
the
blanks.
READ
CAREFULLY!
(25
points)
PART
IV:
Graphing
Linear
Equations
How--To
By
this
point,
you
should
have
an
idea
about
the
elements
of
a
linear
equation,
but
lets
review
and
make
sure
you
could
graph
a
linear
equation
in
any
form.
y = mx + b
y--intercept
slope
The
y--intercept
is
where
you
place
your
first
point.
Remember:
If
there
is
no
y--
intercept,
it
is
simply
0.
From
this
point,
your
slope
tells
you
where
to
move
from
there.
m = rise run
The
number
of
spaces
you
move
UP
or
DOWN
The
number
of
spaces
you
move
RIGHT
Examples:
m = - 1
2
Move
down
1
from
the
y--intercept,
and
2
units
the
right.
m = 5
3
Move
up
5
from
the
y--intercept,
and
3
to
the
right.
m = -3 = - 3
A
whole
number
is
the
same
as
that
number
over
1.
1
Move
down
3
from
the
y--intercept
and
1
to
the
right.
Graphing
Linear
Equations
Tutorial
Example:
Graph
y = - 2 x + 4
3
Step
1:
Identify
the
slope
and
y--intercept.
m
=
b
=
Step
2:
Plot
the
y--intercept
on
the
y--axis.
This
point
is
(0,4)
Step
3:
From
this
point,
move
according
to
the
slope.
m = - 2
3
Move
DOWN
2
from
this
point,
and
then
RIGHT
3.
Step
4:
Connect
your
points
and
make
your
line.
What
if
my
equation
isn't
in
y = mx + b
form?
You'll
have
to
make
it
look
like
something
you
know
how
to
graph,
so
solve
for
y
first.
Example:
Graph
the
equation
5x - 4 y = 16 .
5x - 4y = 16
-5x - 5x
-4y = 16 - 5x
-4y = 16 - 5x -4
y
=
16 - 5x -4
y
=
16 -4
-
5 -4
x
y = -4 + 5 x 4
y= 5x-4 4
Complete
the
next
worksheet.
Be
sure
to
put
your
equation
in
its
proper
form
first,
then
graph.
(15
points)
Part
V:
Using
Linear
Equations
to
Run
a
Business
(15
points)
Snack
Shack
You
decide
to
try
your
luck
as
an
entrepreneur,
and
open
up
the
"Snack
Shack",
which
caters
to
Wood--Ridge
residents
who
love
grilled
cheese
(which
is
all
you
make
at
the
Snack
Shack).
Through
research,
you
find
that
the
cheapest
prices
for
your
supplies
are
as
follows:
Bread:
$1.44/loaf
?
makes
12
sandwiches.
Cheese:
$3.50/bag
?
makes
10
sandwiches.
Butter:
$3.75/lb
?
makes
40
sandwiches
Paper
Towels:
$0.99/roll
?
used
for
120
sandwiches.
Using
the
information
above,
find
the
unit
cost
of
each
item.
(So,
if
bread
is
$1.44
per
loaf,
and
it
makes
12
sandwiches,
how
much
does
bread
cost
for
1
sandwich?)
List
the
information
below:
Bread
Cheese
1.)
How
much
does
it
cost
to
make
1
sandwich?
2.)
Your
cost
curve,
or
how
much
you
money
you
spend
to
run
your
business,
is
$20
for
startup,
plus
the
cost
per
sandwich.
Write
the
equation
you
can
use
to
calculate
your
cost
below.
3.)
You
charge
$1.50
per
sandwich.
Write
the
equation
for
total
revenue
below.
4.)
Graph
both
equations
on
the
same
coordinate
plane
in
different
colors.
Be
sure
to
label
everything.
5.)
How
many
sandwiches
do
you
have
to
sell
to
break
even?
6.)
At
what
point
will
your
profit
exceed
costs
by
100
dollars?
Butter
Paper
Towels
................
................
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