Questions and Answers > Unit 6 portfolio_ MATH MISC. Linear Functions Unit Portfolio. All Answers.

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Name ___________________________ Date ________________________

Linear Functions Unit Portfolio Directions: Complete each of the tasks outlined below.

Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city and research the rates of two different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile.

Task 1 a. For the first company, express in words the amount the cab company charges per ride and per mile. $3.25 per ride and $1.50 per extra 1/9 mile. b. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.

Slope Intercept Form y = mx + b Ex. y = 5x + 65 Ex.

Point – Slope Form

Standard Form

Ax + By = C where A, B, and C are real numbers, and A and B are not both zero.

Ex. 3x + 4y = 24

Your equation ___________y=13.50x+3.25_____________ Why did you choose this equation?

I used slope intercept because I knew the Slope and the y intercept of the line. c. What do the slope and y-intercept mean in the context of this problem? Hint: What do you pay when you step into the cab?

The slope in the equation above means the amount of money you pay per mile. The y intercept represents the flat rate or amount of money charged as soon as you get in the cab.

Task 2

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For the second company, express in a table the cost of the cab ride given the number of miles provided.

Number of Miles Total Cost (dollars)

0

1

2

3

4

5

$4.15

$15.75

$31.50

$47.25

$63.00

$78.75

a. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.

Slope Intercept Form

y = mx + b

Ex. y = 5x + 65 Ex.

Point – Slope Form

Standard Form

Ax + By = C where A, B, and C are real numbers, and A and B are not both zero.

Ex. 3x + 4y = 24

Your equation ____________y=15.75x+4.15____________ Why did you choose this equation?

I choose slope intercept form again because in both equations, the slope and y intercept are easy to identify and apply to the scenario. b. What does the slope mean in the context of the problem?

The slope represents the flat rate or charge of money you pay when you get in the cab.

Task 3 Cabs use a valuable commodity—gas! Research average gas prices from 2005– 2015 for the city you chose. If you can't find this information for your specific city, you can research national gas price averages instead.

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If you use this data you will need to calculate the average. You can do this using a formula in Excel. a. Create a table showing the average gas price each year.

City: __________America town________

Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Average Gas Price 2.295 2.589 2.801 3.266 2.35 2.788 3.527 3.644 3.526 3.367 2.538

b. Create a scatter plot of the data in your table. Don’t forget to label your x and y access with the names of the variables.

2.295 2.589 2.801 3.266 2.35

Prices2.788 3.527 3.644 3.526 3.367 2.538 200 5

200 6

200 7

200 8

200 9

201 0

201 1

201 2

201 3

201 4

2015

Years

c. What equation models the data? Y=0.07x - 151.15 What are the domain and range of the equation?

Domain (range of x values) 2211 Range (range of y values) _1.349_____________________ Do you think your equation is a good fit for the data? Explain how you determined your answers. Yes. I used the T-83 calculator for an accurate data function.

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d. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither?

Negative correlation.

How much do you expect gas to cost in 2020? Explain.

Gas prices are expected to be $10.47. This price is concluded by multiplying the A value with (2020) and subtracting the product from the B value.

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