Linear Equations Project Based Learning

UP or DOWN
The number of spaces you move
RIGHT

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Graphing Linear Equations Tutorial
Example: Graph
y
= −
2
3
x
+ 4
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.

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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
− 4y = 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
4
x
y
=
5
4
x
− 4
Complete the next worksheet. Be
sure to put your equation in its
proper form first, then graph. (15
points)

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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
Butter
Paper Towels
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?