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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