Linear Equations Project Based Learning

Transcription

1 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

2 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?)

3 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) 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.

4 X Equation: (x,y) 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)

5 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 1 A whole number is the same as that number over 1. Move down 3 from the y- intercept and 1 to the right.

6 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.

7 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 = x y = 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)

8 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?) 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? List the information below: Bread Cheese Butter Paper Towels 6.) At what point will your profit exceed costs by 100 dollars?