Class 9 Maths · Original EZT practice
Introduction to Linear Polynomials (Class 9 Chapter 2): summary and practice
Linear polynomials are the degree-1 expressions: what makes them linear, how to spot a linear pattern in a table or sequence, constant-rate growth and decay, and linear relationships between two quantities, seen in tables and on graphs. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. What makes a polynomial linear
A polynomial is linear when its degree is 1 - the variable appears only to the first power. 3x + 2 is linear; 5x^2 + 3x is not, whatever its value of x.
2. Exploring linear patterns
A sequence or table is linear when consecutive values differ by a constant amount. That constant difference is the rate; the starting value is where the pattern begins.
3. Linear growth and linear decay
Adding the same amount each step is linear growth; subtracting it is linear decay. Both produce straight-line behaviour - one climbing, one falling.
4. Linear relationships, visualised
Two quantities linked by a rule like y = 3x + 2 form a linear relationship. Tables show it as constant differences; the graph shows it as a straight line.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Recognise a linear polynomial
Choose the method: Check the highest power of the variable: degree 1 means linear.
EZT practice question
Is 5x^2 + 3x a linear polynomial?
Show the worked solution
- Powers of x present: 2 and 1.
- The highest power - the degree - is 2.
- Linear requires degree exactly 1.
Answer: No - it has degree 2, so it is not linear.
Check: 3x alone would be linear; adding the x^2 term is what breaks linearity. Degree, not the number of terms, decides.
Watch for this: Do not call an expression linear just because it has an x term - any squared term makes the degree 2.
Now try it yourself
Is 7x - 4 linear?
Check your answer
Yes.
Degree 1 - only the first power of x appears.
Solve a linear equation
Choose the method: Collect the variable on one side by undoing operations in reverse.
EZT practice question
Solve 2x + 3 = 11.
Show the worked solution
- Subtract 3 from both sides: 2x = 8.
- Divide by 2: x = 4.
- Done - one solution, as a linear equation should have.
Answer: x = 4.
Check: Substitute back: 2(4) + 3 = 11. The left side matches the right, so x = 4 is correct.
Watch for this: Move terms with their signs flipped - taking 3 across as +3 gives 2x = 14 and a wrong answer.
Now try it yourself
Solve 3x - 5 = 10.
Check your answer
x = 5.
3x = 15, then divide by 3.
Spot a linear pattern
Choose the method: Compute consecutive differences; constant difference means linear.
EZT practice question
Is the pattern 5, 8, 11, 14 linear? If so, what is its rate?
Show the worked solution
- Differences: 8 - 5 = 3, 11 - 8 = 3, 14 - 11 = 3.
- Constant difference 3.
- So the pattern grows linearly at rate 3.
Answer: Yes - linear with constant difference 3.
Check: Predict the next term: 14 + 3 = 17. A constant difference always predicts the next term in one step.
Watch for this: The rate is the DIFFERENCE (3), not the starting value (5) - the two play different roles in the rule.
Now try it yourself
Is 20, 17, 14, 11 linear? Rate?
Check your answer
Yes - decay at rate 3 (difference -3).
Constant difference -3.
Evaluate a linear relationship
Choose the method: Substitute the given x into the rule and compute y.
EZT practice question
For the relationship y = 3x + 2, find y when x = 4.
Show the worked solution
- Replace x by 4: y = 3(4) + 2.
- = 12 + 2.
- = 14.
Answer: y = 14.
Check: Step x from 4 to 5: y goes 14 to 17, a difference of 3 - the coefficient of x, exactly as a linear rule demands.
Watch for this: Multiply before adding: 3(4) + 2 is 14, not 3 x 6 = 18 - order of operations decides.
Now try it yourself
For y = 2x - 1, find y at x = 5.
Check your answer
9.
10 - 1.
Linear growth versus linear decay
Choose the method: Positive constant difference is growth; negative is decay.
EZT practice question
A tank holds 50 litres and loses 4 litres every hour. Is this linear? When is it empty?
Show the worked solution
- Each hour subtracts the same 4 litres - constant difference, so linear decay.
- Level after h hours: 50 - 4h.
- Empty when 50 - 4h = 0, so h = 12.5 hours.
Answer: Linear decay; empty after 12.5 hours.
Check: At h = 12 the level is 50 - 48 = 2 litres; one more half hour removes them. Consistent.
Watch for this: Do not write 50 + 4h for a shrinking quantity - the sign of the rate decides growth or decay.
Now try it yourself
A plant grows 2 cm a week from 10 cm - height after 6 weeks?
Check your answer
22 cm.
10 + 2 x 6.
Build the rule from a table
Choose the method: The constant difference is the coefficient of x; adjust the constant to fit one row.
EZT practice question
A table gives y = 5, 8, 11, 14 at x = 1, 2, 3, 4. Find the rule.
Show the worked solution
- Constant difference 3, so the rule looks like y = 3x + c.
- Fit x = 1, y = 5: 5 = 3 + c, so c = 2.
- Rule: y = 3x + 2.
Answer: y = 3x + 2.
Check: Test another row: at x = 4, 3(4) + 2 = 14 - matches the table.
Watch for this: Do not stop at y = 3x - the constant term is what anchors the rule to the actual values.
Now try it yourself
Table y = 1, 3, 5, 7 at x = 1, 2, 3, 4 - rule?
Check your answer
y = 2x - 1.
Difference 2, and 1 = 2 - 1.
Try a mixed set
Choose a method or explanation before opening each answer.
1. When is a polynomial linear?
Show answer and reason
When its degree is exactly 1.
Only the first power of the variable may appear.
2. Sign of a linear pattern in a table?
Show answer and reason
Constant difference between consecutive values.
The difference is the rate.
3. Linear decay means?
Show answer and reason
Subtracting the same amount each step.
Negative constant difference.
4. Graph of a linear relationship?
Show answer and reason
A straight line.
Constant rate means constant slope.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Solve 3x - 5 = 10.
- The rule for the table 1, 3, 5, 7 at x = 1, 2, 3, 4.
- Is 7x - 4 linear?
Know the rule but lose track of the steps?
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Questions about this practice page
- What makes a polynomial linear?
- Its degree - the highest power of the variable - must be exactly 1. 3x + 2 and 7x - 4 are linear; 5x^2 + 3x is not, because the squared term lifts the degree to 2.
- How does a constant difference signal a linear pattern?
- Adding the same amount at every step is exactly what a degree-1 rule does: in y = 3x + 2, stepping x by 1 always steps y by 3. Constant difference and linear rule are two views of the same thing.
- Is this the same chapter as Polynomials in older Class 9 books?
- No - the older book's Chapter 2 was Polynomials in general. The current Ganita Manjari Part I introduces LINEAR polynomials first, with patterns, growth and relationships; check the chapter title on your book, not just the number.
- What is the difference between linear growth and linear decay?
- Growth adds a constant amount each step (positive difference, line climbing); decay subtracts one (negative difference, line falling). Both are linear - the sign of the rate is the only difference.
- Are these the NCERT exercise questions for Introduction to Linear Polynomials (Class 9)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.