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
1. 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 will be:
C = 2.50m + 2.50
Where C represents the amount charged and m represents the number of miles.
2. 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 to point-slope form, we need to find two points on the line. Let's choose two values for m and calculate the corresponding values for C using the equation C = 2.50m + 2.50:
For m = 0, C = 2.50(0) + 2.50 = 2.50
For m = 1, C = 2.50(1) + 2.50 = 5.00
So, we have two points: (0, 2.50) and (1, 5.00).
Using the point-slope form, which is given by y - y1 = m(x - x1), we will choose one of the points, let's say (0, 2.50):
C - 2.50 = 2.50(m - 0)
Simplifying the equation further:
C - 2.50 = 2.50m
This is the equation in point-slope form to represent the amount charged, C, for m number of miles by the company in Charlotte.
3. 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 eliminate any decimals and fractions. The equation C = 2.50m + 2.50 can be rearranged as:
2.50m + C = 2.50
To eliminate the decimals, we can multiply the entire equation by 100:
250m + 100C = 250
Now, we don't want any fractions, so let's multiply the entire equation by 4:
1000m + 400C = 1000
This is the equation in standard form to represent the amount charged, C, for m number of miles by the company in Charlotte.
4. 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 represents the initial fee or base fare charged by the cab company. It is the amount you pay when you step into the cab, regardless of the number of miles traveled.
In this case, the y-intercept is 2.50. Therefore, when you step into the cab in Charlotte, you would pay a flat fee of $2.50 before considering the per-mile charge.