Using SLOPE AND equations of lines in the real world

The cost of a school banquet is $95 plus $15 for each person attending The cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives the total cost of the number of people attending. What is the cost of 70 people? Use the table to determine if there is a constant rate of change. If there is, state the rate of change and determine if there is a proportional linear relationship. x Y 5 2 10 4 15 Write the equation of a line in slope intercept form: m = 2 ( - 1, 2) What is the slope of a ski run that rises 6 feet for every horizontal change of 24 feet? Graph the line: 4x + 3y = 6

y = mx + b What do you need to find the equation of a line? Take a few minutes to write out answers to the following questions. Be ready to share your answers with your elbow partner. How do you find slope using: a graph a table two points How do you find the y-intercept using: a. a graph b. a table c. two points https://www.youtube.com/watch?v=nfWlot6h_JM

Today you will work in your group to complete a REAL WORLD application task using slope and equations of lines. This assignment is broken up into sections. Each section is timed. Once I call time, be ready to share what your group has recorded on your answer sheet. Everyone in the group must participate. Each of you will be evaluating your participation and I will be too. You will receive a participation grade for today’s lesson out of 50. 25 points will come from your self evaluation and 25 points will come from me.

WRITING EQUATIONS OF LINES FROM SITUATIONS Read the first part of page one. Answer the question: What do you think self-service car wash owners consider when they decide how much to charge a customer? Write out the equations of the lines for: Sudzo Wash and Wax Pat’s Power Wash U-Wash It (5 minutes)

Sudzo Wash and Wax charges customers $0. 75 per minutes to wash a car Sudzo Wash and Wax charges customers $0.75 per minutes to wash a car. Write an equation that relates the total charge c to the amount of time t in minutes. Pat’s Power Wash charges $2.00 per car to cover the cost of cleaning supplies, plus $0.49 per minute for the use of water sprayers and vacuums. Write an equation for the total charge c for any car-wash time t. U-Wash-It charges $10 for each car. The business owners estimate that it costs them $0.60 per minute to provide soap, water, and vacuums for a car. Write an equation for the profit p U-Wash-It earns if a customer spends t minutes washing a car.

Now, using your equations, answer the questions about these car washes. Interpret the slopes and y-intercepts in context with the situations. What questions can the equations help you answer? Which car wash do you think is the best value for money? Why? Justify your answer. (10 minutes)

Now, take about 5 minutes to work on the next situation. Squeaky Clean Car Wash The Squeaky Clean Car Wash charges by the minute. The table shows the charges for several different times. Time (mins) 5 10 15 20 25 Charge ($) $8 $13 $18 $23 $28

Euclid’s Car Wash Look at Euclid’s Car Wash, answer the questions that are posed. Look carefully at the graph. How do you find the equation of a line from a graph? Interpret the equations that you write. You will have about five minutes to do this.

Super Clean Car Wash Super Clean Car Wash Date: 11 – 13 – 13 Start Time: 08:30 am Stop Time: 08:50 am Charge: $12 Super Clean Car Wash Date: 11 – 11 – 13 Start Time: 02:55 pm Stop Time: 03:05 pm Charge: $6 Use the two receipts to answer the questions about Super Clean Car Wash. You will have about 10 minutes to complete this portion of the lesson.

You will now take a few minutes to evaluate your participation in today’s lesson. Look at each category and HONESTLY rate yourself. When you are done, turn your form in to me. https://www.youtube.com/watch?v=CevxZvSJLk8

Ticket out the door………. Now that you have worked through these examples, answer the following questions. Suppose you want to write an equation of the form y = mx + b to represent a linear relationship, what is your strategy if you are given: a description of the relationship in words? two or more (x,y) values or a table of (x,y) values? a graph showing points with co-ordinates?

HOMEWORK Complete Stations 3 and 4 of the review worksheet. Start reviewing for you test on Friday. You may want to go through the power points on the wiki. Remember, tutoring is this Friday at 8am