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.
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 the equation in point-slope form, we need to identify a specific point through which the line representing the cab fare passes and the slope of the line. The point-slope form of an equation is given by:
\( y - y_1 = m(x - x_1) \)
where \( (x_1, y_1) \) is the point and \( m \) is the slope.
Since the cab company charges a flat fee of $1.95 for pickup, this is the starting cost, and it occurs at zero miles. Therefore, we can use the point \( (0, 1.95) \).
The company then charges $2.70 per mile traveled, so the slope of the line representing the cost is $2.70 per mile; thus, the slope \( m \) is 2.70.
Now substituting the point and the slope into the point-slope formula, we get:
\( C - 1.95 = 2.70(m - 0) \)
Simplifying, this equation becomes:
\( C - 1.95 = 2.70m \)
This is the point-slope form of the equation, representing the amount charged, \( C \), for \( m \) number of miles for the cab ride in Raleigh, NC.