Writing Linear Equations for Real World Scenarios

Writing Linear Equations for Real World Scenarios

Goals of lesson

• Identify rates of change and one-time/beginning values in a scenario

• Write linear equations to represent real world scenarios

In order to write an expression or equation to represent a situation, you must consider the following:

The value that can happen multiple times is the rate of change

The one time or beginning value happens only once

Let's look at the values to practice identifying those that happen only once (or beginning value) and those that can happen more enough (rate of change)

Keep in mind that there does not have to be a one-time/beginning value!

Also, a little hint: "per" is a keyword indicating multiplication

Multiple Choice

A car salesperson earns $300 per week and $50 for each car sold that week.

True or false:

The number of cars sold that week affects (changes) the salesperson's weekly pay

• True

• Falso

Multiple Choice

A car salesperson earns $300 per week and $50 for each car sold that week.

What is the value associated with the change?

• 300

• 50

Multiple Choice

A car salesperson earns $300 per week and $50 for each car sold that week.

Is there a one-time value associated with the weekly pay?

• Yes

• No

Multiple Choice

A car salesperson earns $300 per week and $50 for each car sold that week

What is the one-time value associated with the weekly pay?

• 300

• 50

Practice Time!

Identifying Rates of Change and One-time/Beginning Values Partner Match Up

Writing and Solving Equations to Model and Solve Real Scenarios

1. Read the problem at least twice.

- first, to understand the situation and identify the question

- next, to identify the important information (highlight, underline or list)

2. What are your variables?

3. Write the equation to model the problem

- you may want to write this out in words first

4. Solve the equation

*** Write your final answer in sentence form ***

To write an expression (needed for the equation) use the form: mx + b

m is the value for the rate of change

b is the one time or beginning value

Example: Scoots Inc. charges $20 to rent a moped for the day and $0.50 per mile driven

Multiple Choice

Scoots Inc. charges $20 to rent a moped for the day and $0.50 per mile driven

What is the b (one-time/beginning value)?

• 20

• 0.50

Multiple Choice

Scoots Inc. charges $20 to rent a moped for the day and $0.50 per mile driven

What is the rate of change (can happen more than once)?

• 20

• 0.50

Multiple Choice

Scoots Inc. charges $20 to rent a moped for the day and $0.50 per mile driven

What is the expression that represents the cost of the rental?

• y = 20x + 0.50

• y = 0.50x + 20