Cab companies often charge a flat fee for picking someone up and then an additional fee per mile driven. The city of Charlotte, NC charges a $2.50 fee and and $2.50 per mile for each can ride.
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)
The point-slope form of a linear equation is written as:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. In this scenario, the total cost \( C \) depends on the number of miles \( m \) driven. Since there's a flat fee and a fee per mile, the total cost can be calculated as:
\[ C = \text{flat fee} + (\text{cost per mile}) \times m \]
From the information provided, the flat fee is $2.50 and the cost per mile is also $2.50. Thus:
\[ C = 2.50 + 2.50 \times m \]
Now, to get this into point-slope form, we need to plug in a specific point. Let's choose when \( m = 1 \) (one mile), which would correspond to a cost of:
\[ C = 2.50 + 2.50 \times 1 = 5.00 \]
So, the point (1, 5) represents driving one mile and being charged $5.00 in total. Now we can insert this point into the point-slope form, where the slope (rate of change) is $2.50 per mile:
\[ C - 5 = 2.50(m - 1) \]
This is the point-slope form of the equation that represents the amount charged, \( C \), for \( m \) number of miles by the cab company in Charlotte, NC.