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.
b. Write an equation in slope-intercept, point-slope, or standard form. Explain
why you chose the form you did.
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?
Task 2
For the second company, express in a table the cost of the cab ride given the
number of miles provided.
Number
of Miles
0 1 2 3 4 5
Total
Cost
(dollars)
a. Write an equation in slope-intercept, point-slope, or standard form. Explain
why you chose the form you did.
b. What does the slope mean in the context of the problem?
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.
a. Create a table showing the average gas price each year.
b. Create a scatter plot of the data in your table.
No, its really confusing, i emailed my teachers about it but their in instructions are still confusing. Please help it was due yesterday an i still have a lot more other portfolios to do.
So I came here for answers but y’all are clueless so I’ll explain how to do it💀
It wants you to find two cab company’s AKA taxi company’s, which ones you pick can be from any USA city but both have to be from the same city. Insure that both charge different amounts of money per mile and also have different flat fees. (Flat fees are what you pay right away, so like for example say it costs $15 to get in the cab and $5 for every mile the equation would be something like y = $15 + $5x (x in that case would be however many miles you traveled.)
to make it all easier it gives the option to make up the price as long as you think it is reasonable so you can make all the prices equivalent to make the equations later on easier to do.
**TASK 1**
A. Pick the first company you want to do and in express in word form how much the Cab company charges per start of ride and per mile.
Going back to the example I gave (y = $15 + $5x) you just express it in word form so that would be something like “the cab company charges 15 bucks upfront and per mile you are charged an extra 5 bucks”
B. I’m doing slope intercept form for this one, Y is gonna be the cost once the trip is completely over, X is however many miles where traveled and the variable without any letters is the upfront cost. Using my equation from before that would make it y = $15 + $5x
C. What do the slope and y intercept form mean in the context of this problem? Y is the upfront cost while X is how many miles you went.
**TASK 2**
A. Write an equation in slope intercept form (or any other form) . Explain why you chose the form you did.
To do this one change the numbers up however you’d like to while following the same guidelines then your half done. For the next bit give your reasoning, my reasoning would be that it is much simpler to do slope for me which is why I chose it.
**TASK 3**
A. In this it wants you to create a table for this of gas prices, I’d do the National gas prices from 05-15 as instructed and put it into a table. One column of the table is each passing year and the other column is the different price for that respective year.
B. Create a scatter plot of the data in your table. This one may seem a bit trickier if your lazy like me but trust me this is simple to do. Go on google and find a good template of a empty scatter plot. Assuming you guys have snapchat or some drawing app open the image in it and plot down the points for each gas price and their year.
C. To find the equation that models the data id find about the average it went up every year. To find the domain you find how many the set of inputs (the numbers involved for price) and put it down. Range is the biggest number subtracted by the smallest number of inputs. So let’s say the biggest was 20 and smallest was 5, the range of that would be 15. And for explaining why u think it is a good fit and how u determined the answers I’d explain how u did the equations and show how that justifies it.
D. If there is a trend in it like a reoccurring pattern put it down. If there is a positive, negative or no correlation between them put that down too.
And then give your best guess as to what gas prices would be in 2020
I hope that helps you guys out!!
has anyone finished this?
Thanks enbi!!!
To complete the tasks outlined in the Linear Functions Unit Portfolio, follow these steps:
Task 1:
a. Research two different cab companies in a U.S. city and find their rates per ride and per mile. If you cannot find this information, you can make up reasonable prices for the flat rate and rate per mile.
For example:
Company A charges a flat rate of $5 per ride and an additional $2 per mile.
Company B charges a flat rate of $10 per ride and an additional $1.50 per mile.
b. Write an equation in slope-intercept, point-slope, or standard form. Choose the form that best represents the given information and is most convenient for solving the problem.
The equation in slope-intercept form for Company A can be written as:
y = 2x + 5, where y is the total cost and x is the number of miles.
c. In the context of this problem, the slope represents the rate charged per mile. In the equation, the slope is 2, which means that for every mile traveled, $2 will be added to the total cost. The y-intercept, 5, represents the flat fee charged when stepping into the cab.
Task 2:
a. Create a table with the number of miles as the input and the total cost (in dollars) as the output. Calculate the total cost for different numbers of miles, using the rates provided by the second cab company.
Example:
For the second company:
Number of Miles:
0, 1, 2, 3, 4, 5
Total Cost:
$8, $9.50, $11, $12.50, $14, $15.50
b. Write an equation in slope-intercept, point-slope, or standard form. Choose the form that represents the given information.
The equation in point-slope form for the second company can be written as:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.
Using the points (1, 9.50) and (5, 15.50), the equation becomes:
y - 9.50 = 1.50(x - 1)
Simplifying, we get:
y = 1.50x + 8
In the context of this problem, the slope (1.50) represents the rate charged per mile. For every mile traveled, $1.50 will be added to the total cost.
Task 3:
a. Research the average gas prices from 2005-2015 for the city you chose. If you cannot find this information for your specific city, you can research national gas price averages instead.
Create a table showing the average gas price for each year.
Example:
Year Average Gas Price (dollars)
2005 $2.50
2006 $2.75
2007 $3.00
2008 $3.50
...
2015 $4.25
b. Create a scatter plot of the data in your table, with the year on the x-axis and the average gas price on the y-axis. Each data point represents the gas price for a specific year. Use a graphing tool or software to plot the points and visualize the trend in gas prices over time.
Ok since no one wants to answer I will help in a minute
So, have you done the first step?
Pick a U.S. city and research the rates of two different cab companies in that city.