Writing Linear Equations from Word Scenarios

In this lesson, we will learn how to write linear equations based on word problems. A linear equation can typically be expressed in the slope-intercept form, which is given by the formula:

$y = mx + b$

where $m$ represents the slope and $b$ represents the y-intercept. To write an equation from a word problem, identify the variables, the relationship between them, and the constants involved.

Example:

Problem: A store sells notebooks for $2 each and pens for$1 each. If a student buys $n$ notebooks and $p$ pens, and spends a total of $10, write a linear equation representing this scenario.

Step 1: Identify the variables

• Let $n$ be the number of notebooks.
• Let $p$ be the number of pens.

Step 2: Determine the costs

• The cost for notebooks is $2n$.
• The cost for pens is $1p$ (or $p$).

Step 3: Write the equation based on total cost

The total cost is given as $10$, so we can set up the equation:

$2n + p = 10$

This equation represents the total amount spent on notebooks and pens.

Key Questions:

• What is the slope in the equation $y = 3x + 4$?
• How can you express the equation for a total of $15 spent on$5$items if one item costs$2$?
• If a car rental company charges a flat fee of $20 plus$0.50 per mile, how would you write the equation for the total cost $C$ in terms of miles driven $m$?
• In a situation where $y$ increases by $4$ for every $1$ increase in $x$, what is the slope of the line?

Keywords:

• Linear Equation
• Slope-Intercept Form
• Variables
• Constants
• Word Problems