Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven the city of raleigh nc charges $1.95 fee and $2.70 per mile for each cab ride
6. For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles.
To create a table representing the cost of the cab ride for the Raleigh company at different distances:
| Miles | Cost |
|-------|------|
| 5 | $14.25 |
| 10 | $29.50 |
| 15 | $44.75 |
| 20 | $60.00 |
The cost for a 15-mile cab ride would be $44.75.
7. For the Raleigh company write an equation in slope-intercept form to represent the amount charged, C, for m number of miles.
To write an equation in slope-intercept form to represent the amount charged for a certain number of miles, we can use the formula:
C = (m * $2.70) + $1.95
Where:
C is the amount charged for the cab ride
m is the number of miles
This equation represents the flat fee of $1.95 plus the additional fee of $2.70 per mile.
8. For the Raleigh company write an equation in point-slope form to represent the amount charged, C, for m number of miles for the company in Raleigh, NC.
To write an equation in point-slope form to represent the amount charged for a certain number of miles, we can use the formula:
C - C1 = m * (C2 - C1)
Where:
C is the amount charged for the cab ride
m is the number of miles
C1 and C2 are the known costs for two points
Let's use the points (5, $14.25) and (10, $29.50) to write the equation:
C - $14.25 = m * ($29.50 - $14.25)
Simplifying the equation further:
C - $14.25 = m * $15.25
This equation represents the change in cost per mile multiplied by the number of miles traveled.
9. Write an equation in standard form to represent the amount charged, C, for m number of miles for the company in Raleigh.
To write an equation in standard form to represent the amount charged for a certain number of miles, we need to rearrange the point-slope form equation from the previous steps. Starting from the equation:
C - $14.25 = m * $15.25
Let's rewrite it:
C = m * $15.25 + $14.25
To convert it into standard form, we need to eliminate the decimals and constants. Multiply the entire equation by 100 to remove the decimals:
100C = 1525m + 1425
To further simplify, let's rearrange and group like terms:
-1525m + 100C = 1425
Thus, the equation in standard form representing the amount charged, C, for m number of miles for the company in Raleigh, NC is -1525m + 100C = 1425.