Class 10 Maths Chapter 4 Exercise 4.2 Solutions 2026 – Functions and Graphs Notes PDF

Unit 4: Functions and Graphs | Exercise 4.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 4.2 solutions for Functions and Graphs have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Turning a Formula into a Picture

A function like f(x) = 2x + 3 is just a rule on paper until it’s plotted — once graphed, patterns that are hard to see in the algebra become immediately obvious. Exercise 4.2 teaches the standard method for graphing a linear function: build a table of values, plot the points, and join them to reveal a straight line.

Key Concepts Covered in Exercise 4.2

Building a Table of Values

To graph y = mx + c, choose a handful of simple x-values, substitute each into the equation, and record the corresponding y-value. Three points are usually enough to confirm a straight line, though more can be used for accuracy.

Slope and Y-Intercept

In y = mx + c, m is the slope (how steeply the line rises or falls) and c is the y-intercept (where the line crosses the y-axis, at x = 0). Recognizing these two values directly from the equation makes sketching faster than plotting many points.

Plotting and Joining Points

Each (x, y) pair from the table becomes a point on the coordinate plane. For a linear function, these points always lie in a perfectly straight line, which can then be drawn with a ruler through all the plotted points.

Reading Values Off the Graph

Once drawn, a graph can answer questions the equation alone makes tedious — such as finding y for a given x, or x for a given y, just by tracing lines to the axes.

Step-by-Step Solved Examples

Q. No. 1: Complete a table of values for y = 2x + 1 using x = −1, 0, 1, 2.

x = −1: y = 2(−1)+1 = −2+1 = −1

x = 0: y = 2(0)+1 = 0+1 = 1

x = 1: y = 2(1)+1 = 2+1 = 3

x = 2: y = 2(2)+1 = 4+1 = 5

Table: (−1,−1), (0,1), (1,3), (2,5)

Q. No. 2: State the slope and y-intercept of y = −3x + 4.

Comparing with y = mx + c:

Slope, m = −3

Y-intercept, c = 4 (the line crosses the y-axis at (0, 4))

Q. No. 3: Using the table from Q. No. 1, find the value of x when y = 3, without recalculating.

From the table, the pair (1, 3) already shows y = 3 when x = 1.

So when y = 3, x = 1.

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 4.2 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on identifying the slope or y-intercept from a given linear equation
• Short Questions: Completing a small table of values for a given linear function
• Long Questions: Full graph sketching from a table of values, with points plotted and labeled

Where This Matters Beyond This Exercise

The table-of-values method used here is exactly the same technique applied to quadratic functions in the next exercise, just with a curved rather than straight result. Graphing linear relationships is also a core skill in economics (supply and demand curves), physics (distance-time graphs), and everyday data analysis.

Common Mistakes Students Make in Exercise 4.2

• Making an arithmetic error when substituting negative x-values into the equation
• Confusing the slope and the y-intercept when reading them from y = mx + c
• Plotting points with x and y swapped, especially when the table is read across instead of down
• Drawing a line that doesn’t pass exactly through all the plotted points

Why This Exercise Matters for the Board Exam

Graph-sketching questions are usually worth several marks and are graded on both the table of values and the accuracy of the final graph, making careful, step-by-step working essential. Reading values off a completed graph is also a common follow-up question, so practicing this skill alongside the sketching itself is worthwhile.

Quick Links – Chapter 4: Functions and Graphs

Links for sections other than Exercise 4.2 will be activated as they are published on this site.

Download Exercise 4.2 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 4.2 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. How many points do I need to graph a linear function?

Technically only two points are needed to draw a straight line, but using three or more is recommended as a check — if all the points don’t line up perfectly, it signals a calculation error in the table of values.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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