Linear Word Problems – Real-World Applications
Everything covered in this section – constant rates of change, function tables, writing y = mx + c, and reading gradients – comes together in real-world linear word problems. The core skill is translating a word description into a linear equation or rate, then using it to answer a specific question, exactly the same translation process you used for word problems throughout this course.
These problems usually describe a starting value (like a flat fee or starting amount) combined with a constant rate (like a cost per unit or a rate of drainage) – the same m and c you've been working with all along, just dressed up in a real-world story.
Solving Linear Word Problems
Identify the starting value (c) and the constant rate (m) from the story, then apply total = starting value + (rate × quantity), or solve for the quantity that gives a specific total.
15 + (3 × 8) = 15 + 24 = $39.
60 ÷ 12 = 5 minutes.
Real-Life Application
- Budgeting: calculating total cost from a fixed fee plus a variable rate.
- Travel planning: calculating fuel remaining over a journey.
- Business: calculating break-even points from fixed and variable costs.
Key Takeaways
- Linear word problems combine a starting value with a constant rate.
- Translate the story into y = mx + c, then solve for the value asked.
- This applies everything learned earlier in this section to real-world contexts.
Practice: Linear Word Problems
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