While the speed limit for rural state highways in New Jersey is 55 miles per hour, the speed limit drops to 35 mph near most of the towns situated along rural state roads. Many towns impose significant fines for speeding.
The table below shows the fine, F, for speeds over the 55 mph limit on the rural state highway within the jurisdiction of the town of Hicksville.
You should know that in Hicksville the fine is found by charging a fixed amount for each mile per hour the speeder exceeds the 55 mph limit, plus a $35 processing fee.
Speed (S, mph) 62 68 75 83 Fine (F, $) 140 230 335 455
- What would the fine be for doing 70 mph in the 55 mph zone?
- When the fine is written as a linear function of the speed and fine in "y = mx + b" form, what is the meaning of the slope and y-intercept?
- Write the formula in a form that clearly shows the processing fee as well as how fast over the limit the speeder was going.
- Assuming that the same type of formula is used throughout Hickesville, what would the fine be if you were caught traveling those same speeds in the 35 mph zone of Hickesville?
- In New Jersey, like in many other states, the fines are doubled for speeding in sections of highway that have a 65 mph posted speed limit. What formula would you use to calculate fines for speeding in the 65 mph zones?
Enter the data from the table into lists on the TI-83 Plus. To simultaneously calculate a regression equation and ready it for graphing, use the following sequence of keystrokes:
[STAT] >> CALC >> (choose a regression model) >> [2nd]-[L1] >> [,] >> [2nd]-[L2] >> [,] >> [VARS] >> Y-VARS >> 1:Function >> [ENTER] >> (specify Y#) >> [ENTER] >> [ENTER].