denise124
denise124 May 15, 2026 • 0 views

Real-world examples of linear relationships for 7th grade

Hey there! 👋 Learning about linear relationships can seem a bit abstract, but they're actually all around us! Let's explore some real-world examples and then test your knowledge with a quick quiz. Ready to dive in? 🤓
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heather.edwards Dec 27, 2025

📚 Quick Study Guide

  • 📈 Definition: A linear relationship is a relationship between two variables that can be represented by a straight line on a graph.
  • Equation: The general form of a linear equation is $y = mx + b$, where:
    • $y$ is the dependent variable.
    • $x$ is the independent variable.
    • $m$ is the slope (rate of change).
    • $b$ is the y-intercept (the value of $y$ when $x = 0$).
  • 🏃‍♀️ Constant Rate of Change: Linear relationships have a constant rate of change, meaning for every unit increase in $x$, $y$ increases (or decreases) by the same amount.
  • 🍕 Real-World Examples: Think about earning money per hour, distance traveled at a constant speed, or the cost of buying multiple items at a fixed price.

✏️ Practice Quiz

  1. A taxi charges a flat fee of $3 plus $2 per mile. Which equation represents the total cost (y) for x miles?
    1. $y = 3x + 2$
    2. $y = 2x + 3$
    3. $y = x + 5$
    4. $y = 5x$
  2. A plant grows 1.5 inches per week. If it was initially 4 inches tall, what equation models its height (y) after x weeks?
    1. $y = 4x + 1.5$
    2. $y = 1.5x + 4$
    3. $y = 5.5x$
    4. $y = 2.5x + 4$
  3. Sarah saves $10 each week. She started with $20. Which equation represents her total savings (y) after x weeks?
    1. $y = 20x + 10$
    2. $y = 10x + 20$
    3. $y = 30x$
    4. $y = 10x - 20$
  4. A baker sells cookies for $1.50 each. If someone buys x cookies, which equation represents the total cost (y)?
    1. $y = x + 1.50$
    2. $y = 1.50x$
    3. $y = 2.50x$
    4. $y = x - 1.50$
  5. A pool is being filled at a rate of 3 gallons per minute. If it already has 10 gallons, what equation models the total gallons (y) after x minutes?
    1. $y = 10x + 3$
    2. $y = 3x + 10$
    3. $y = 13x$
    4. $y = 7x$
  6. John walks at a constant speed of 2 miles per hour. How far (y) will he walk in x hours?
    1. $y = x + 2$
    2. $y = 2x$
    3. $y = 3x$
    4. $y = x - 2$
  7. A phone plan costs $25 per month plus $0.10 per text message. What is the total cost (y) for x text messages in a month?
    1. $y = 25x + 0.10$
    2. $y = 0.10x + 25$
    3. $y = 25.10x$
    4. $y = 24.90x$
Click to see Answers
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  2. B
  3. B
  4. B
  5. B
  6. B
  7. B

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