Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven.
The city of Charlotte, NC charges $2.50 fee and $2.50 per mile for each cab ride.
Write an equation in slope-intercept form to represent the amount charged, C, for m number of miles by the company in Charlotte.
The equation in slope-intercept form that represents the amount charged, C, for m number of miles by the company in Charlotte can be written as:
C = 2.50m + 2.50
Write an equation in point-slope form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Hint: Go to Desmos and convert the equation you created in #1 to a table. Use a point from the table)
To convert the equation C = 2.50m + 2.50 to point-slope form, we need to find a specific point on the line. Let's use the point (0, 2.50).
The point-slope form of an equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Using the point (0, 2.50), we can rewrite the equation in point-slope form:
C - 2.50 = 2.50(m - 0)
Simplifying further, we get:
C - 2.50 = 2.50m
This is the equation in point-slope form representing the amount charged, C, for m number of miles by the company in Charlotte.
Write an equation in standard form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Remember A cannot be negative and no fractions or decimals for any of the values)
To write the equation in standard form, we need to rearrange the equation C = 2.50m + 2.50 to have the variables on one side and the constant term on the other side.
C = 2.50m + 2.50
Subtract 2.50m from both sides:
-2.50m + C = 2.50
Rearrange the terms:
2.50m - C = -2.50
Since we cannot have a negative coefficient for m in standard form, we can multiply both sides of the equation by -1:
-2.50m + C = -2.50
Now, multiplying both sides by -1:
2.50m - C = 2.50
This is the equation in standard form representing the amount charged, C, for m number of miles by the company in Charlotte.
What does the y-intercept mean in the context of this problem? Hint: What do you pay when you step into the cab?
In the context of this problem, the y-intercept of the equation represents the fixed fee charged by the company when you step into the cab or begin the ride. In this case, the y-intercept of the equation is 2.50, which means that when you step into the cab (even if you travel zero miles), you will be charged $2.50 as the initial fixed fee.
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven.
The city of Charlotte, NC charges $1.95 fee and $2.70 per mile for each cab ride.
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.
For the Raleigh cab company charging $1.95 fee and $2.70 per mile, we can create a table to represent the cost of the cab ride for different numbers of miles:
| Miles (m) | Cost (C) |
|-----------|---------|
| 5 | $15.45 |
| 10 | $30.95 |
| 15 | $46.45 |
| 20 | $61.95 |
The cost for the cab ride for 15 miles is $46.45.