NCERT Ganita Manjari, Class 9, textbook pages 16–40 (Part I)

How to help your child with Class 9 Maths Chapter 2, Introduction to Linear Polynomials, at home

Linear expressions, graphs and zeros, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

y = 12x + 50: a straight line

NCERT Class 9 Maths Chapter 2 Introduction to Linear Polynomials: what it teaches

Your teen studies expressions like 2x + 3: their value for different x, their straight-line graphs, the slope (rate of change) and the zero (where the line crosses the x-axis). Real situations like taxi fares follow linear rules.

Why it matters later. Linear polynomials lead to linear equations in two variables and polynomials in Class 10.

See it: this chapter in pictures

x (km): 0 1 2 3fare: 50 62 74 86+12 each km
Constant change means a straight line.
2x − 6 = 0x = 3zero of the polynomial
The zero is where the graph crosses the x-axis.
plans cross: same cost
Where lines cross, costs are equal.

You need

  • graph paper
  • a taxi or phone-plan price list
  • a calculator

Tonight’s 30 minutes

  1. Taxi fare: ₹50 + ₹12 per km. Write it as a linear polynomial: 12x + 50.
  2. Make a table for x = 0 to 5 and plot the points. Are they on a line?
  3. Find the zero of 2x − 6 (x = 3) and see where the graph crosses the x-axis.
  4. Compare two plans: which is cheaper for 10 km?

Words to use

  • linear polynomial
  • coefficient
  • constant
  • graph
  • slope
  • zero

Watch for

  • Plotting too few points and drawing curves. Plot at least three points; linear graphs are straight.
  • Mixing up slope and intercept. Slope is the multiplier of x; intercept is the constant.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouWhere does 2x − 6 cross the x-axis?

Your childAt x = 3.

A game for this week: Plan chooser

  1. Make two price plans (fixed + per unit).
  2. Graph both.
  3. Find where they cross.
  4. Decide which is better for different usage.

A 5-day plan, 30 minutes a day

  1. Day 1Write a linear rule.
  2. Day 2Table and graph.
  3. Day 3Zeros.
  4. Day 4Compare plans.
  5. Day 5Plan chooser.

Everyday moments to practise

  • Taxi fares.
  • Phone plans.
  • Salary plus commission.
  • Temperature conversion.

Quick check

Ask these at the end of the week. Tap to see the answer.

Zero of 2x − 6?

x = 3.

Value of 12x + 50 at x = 5?

110.

Slope of y = 3x + 1?

3.

Ready for the next chapter when your child…

  • Writes linear polynomials for situations.
  • Draws their graphs.
  • Finds zeros and slopes.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

What is a linear polynomial?

An expression like ax + b with a ≠ 0.

What is the zero of a polynomial?

The x-value that makes it 0.

Why is the graph a straight line?

The value changes by the same amount for each step in x.