Real-World Linear Relationships
A real-world linear relationship is a situation where two quantities change at a constant rate and can be represented by a linear equation such as ax + by = c or y = mx + b.
In one line: Fixed amount stays once; rate repeats with quantity.
Practice This ConceptUnderstand it
Many daily-life situations can be modelled using linear equations, such as total cost, distance at constant speed, or marks from fixed scoring rules. The coefficient often shows the rate of change, while the constant may show a starting value or fixed charge.
Example
Formula and rule
Common model: total = fixed amount + rate × quantity, written as y = mx + b when one quantity depends on another.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A shop charges Rs 20 for packing and Rs 50 per item.
- 1For x items, total cost C = 50x + 20.
- 2For 4 items, C = 50(4) + 20 = Rs 220.
Method you can reuse
Visual tip
A table or simple line graph can show how the total changes by the same amount each time the quantity increases by 1.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
A notebook costs Rs 30. How can the cost of x notebooks be written as a linear expression?
Think first, then show answerHide answer
Common wrong answer
For a fixed charge of Rs 40 and Rs 12 per km, students may write C = 40x + 12, wrongly multiplying the fixed charge by distance.
Don't mix this up
Exam tip
Real-World Linear Relationships diagram
Open full screen to read every label clearly.
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
A real-world linear relationship is a situation where two quantities change at a constant rate and can be represented by a linear equation such as ax + by = c or y = mx + b.
- 2
Add for 2 marks
Example: If a taxi charges Rs 40 fixed and Rs 12 per kilometre, the cost for x kilometres can be written as C = 12x + 40.
- 3
Add for 3 marks
The coefficient often shows the rate of change, while the constant may show a starting value or fixed charge.
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