A police department issues speeding tickets using a formula that results in a $135 ticket for speeding 5 miles per hour over the limit and a $180 ticket for speeding 8 miles per hour over the limit.
The slope of the formula used to determine the ticket amount is
the change in ticket amount divided by the change in speed, or the ratio of the ticket amount change to the speed change.
Let's say x represents the speed over the limit in miles per hour.
To determine the slope, we need to find the change in ticket amount and the change in speed for the two given scenarios.
For speeding 5 miles per hour over the limit:
Ticket amount = $135
Speed over the limit = 5 miles per hour
For speeding 8 miles per hour over the limit:
Ticket amount = $180
Speed over the limit = 8 miles per hour
To find the change in ticket amount, we subtract the initial ticket amount from the final ticket amount:
Change in ticket amount = $180 - $135 = $45
To find the change in speed, we subtract the initial speed from the final speed:
Change in speed = 8 miles per hour - 5 miles per hour = 3 miles per hour
Now we can calculate the slope:
Slope = Change in ticket amount / Change in speed
Slope = $45 / 3 miles per hour
Slope = $15 per mile per hour
Therefore, the slope of the formula used to determine the ticket amount is $15 per mile per hour.