Writing Linear Equations from Word Scenarios

In this lesson, we will learn how to translate word problems into linear equations. A linear equation is an equation of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Steps to Write Linear Equations

1. Identify the Variables: Determine what the variables represent in the context of the problem.
2. Determine the Relationship: Look for keywords that indicate operations (e.g., total, more than, less than).
3. Write the Equation: Use the information gathered to formulate the equation.

Example Problem

Scenario: A movie theater charges $10 per ticket. If you buy $x$ tickets, how much will you spend in total?

Step 1: Identify the Variables

• Let $y$ be the total cost.
• Let $x$ be the number of tickets purchased.

Step 2: Determine the Relationship

• The total cost is $10 \times the number of tickets: $y = 10x$.

Step 3: Write the Equation

The linear equation based on the scenario is:

$$y = 10x$$

Key Questions

• What do the variables represent in the word problem?
• How do specific words in the scenario help you determine the operations?
• Can you identify the slope and intercept from the linear equation?

Practice Problems

1. A taxi charges a base fare of $3 plus $2 per mile. Write the equation for the total fare $y$ based on the miles $x$ traveled.
2. You have $50 to spend on notebooks that cost $5 each. Write an equation for the number of notebooks $y$ you can buy if you spend all your money.

Summary

Understanding how to write linear equations from word scenarios is essential for solving real-world problems. Practice identifying variables and forming equations based on different contexts.