Question

A pilot takes a taxi from the airport to a hotel. The taxi driver charges a $4.50 initial charge plus $1.65 per mile. Write an equation that can be used to find y, the total cost of the trip, if x represents the number of miles of the trip?

Answer 1

y = 1.65x + 4.50

Explanation:

We can create a linear equation using the variables given to us to represent this situation.

Linear Equations

Most linear equations are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.

In context, slope is the cost per mile. That is because the number of miles in the variable in this equation and the cost per mile is the rate at which the variable increases. The y-intercept is the initial charge. That is because the total cost starts a $4.50, even if you haven't gone anywhere yet. Additionally, the initial cost does not change at any point, so it should be a constant.

So, now we can plug the values into slope-intercept form to create a linear equation. (Remember m = 1.65 and b = 4.50)

• y = 1.65x + 4.50

Solving the Equation

Now that we set up the equation we can solve for y, at different x-values. This means, given the number of miles, we can find the total cost of the trip. We can do this by substituting x-values into the equation.

For example, let's say that a pilot took a 4-mile taxi ride.

First, plug 4 in for x.

• y = 1.65(4) + 4.50

Then, simplify.

• y = 6.6 + 4.50

Finally, add the terms together.

• y = 11.1

This means if a pilot takes a 4-mile taxi ride, then it will cost $11.10.