# Taxi Service

## Warm-up 1

Describe each element in the equation . Be sure to explain how each variable is represented in multiple representations.

## Warm-up 2

What is the equation of the line that intersects the y-axis at and has a slope of ?

## Learning Objective

Today we will explore how a system of linear equations can be used to exactly solve a real world problem.

## Video Reflection

Write your definition of a System of Equations. Don't worry if you are not exact, and don't worry about how to solve them -- just write what the video made clear to you. Also include a question to ask Mr. Aguilar.

## The Sitch:

You are flying to LaGuardia Airport in New York. You want to take a taxi to drive you from the airport to the World Trade Center. Friends have recommended two taxi services, Gallant Luxury Services and A1 Taxi Service. You call both services and learn they offer the following rates: Gallant: $4 to pick you up and$0.40 for every mile driven. A1 Taxi: $2.50 to pick you up and$0.50 for every mile driven. Your task is to write and solve a system of equations to justify which taxi service would be the most cost effective.

## Write a System of Equations.

Write an equation that represents the cost of using each taxi service. Be sure to define your variables (what does x and y represent?). Notice that because x and y are in both equations and represent the same thing, you will have a system of equations.

## Brainstorm 1

There are a few ways to find when the two taxi services will cost the same (i.e., solving the system of equations). Before we formally learn methods, discuss ideas on how you and your partner would approach finding when both services cost the same. After your discussion, describe the method you two would use.

## Brainstorm 2

Remember the question: Which service would you use to travel from LaGuardia Airport to the World Trade Center? What information do you still need? After you and your partner come up with an idea, write what you need, and then open a new browser to find that information. Record your idea and finding below.

Use the GeoGebra graphing tool below to solve your system of equations. Write your solution to the system below. Be sure that your response answers the question: Which Taxi Service should you use to drive you from the airport to your destination?

## Continuation

After you have visited the World Trade Center, you decide you want to go to the New York Aquarium in Brooklyn. Which service would you use this time? Be sure to justify your answer.