Real-world examples of linear relationships for 7th grade

Question

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? 🤓

heather.edwards · Accepted Answer

📚 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

A taxi charges a flat fee of $3 plus $2 per mile. Which equation represents the total cost (y) for x miles?
        
            $y = 3x + 2$
            $y = 2x + 3$
            $y = x + 5$
            $y = 5x$

A plant grows 1.5 inches per week. If it was initially 4 inches tall, what equation models its height (y) after x weeks?
        
            $y = 4x + 1.5$
            $y = 1.5x + 4$
            $y = 5.5x$
            $y = 2.5x + 4$

Sarah saves $10 each week. She started with $20. Which equation represents her total savings (y) after x weeks?
        
            $y = 20x + 10$
            $y = 10x + 20$
            $y = 30x$
            $y = 10x - 20$

A baker sells cookies for $1.50 each. If someone buys x cookies, which equation represents the total cost (y)?
        
            $y = x + 1.50$
            $y = 1.50x$
            $y = 2.50x$
            $y = x - 1.50$

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?
        
            $y = 10x + 3$
            $y = 3x + 10$
            $y = 13x$
            $y = 7x$

John walks at a constant speed of 2 miles per hour. How far (y) will he walk in x hours?
        
            $y = x + 2$
            $y = 2x$
            $y = 3x$
            $y = x - 2$

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?
        
            $y = 25x + 0.10$
            $y = 0.10x + 25$
            $y = 25.10x$
            $y = 24.90x$

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Real-world examples of linear relationships for 7th grade

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📚 Quick Study Guide

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